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Understanding Statistics In the Behavioral Sciences 9th Edition by Robert R. Pagano – Test Bank
Chapter 1—Statistics and Scientific Method
MULTIPLE CHOICE
- Which method of knowing is used in the following example? An individual accepts as true that there is an afterlife because a minister asserts such is the case.
a. | Method of Authority |
b. | Method of Intuition |
c. | Scientific Method |
d. | Rationalism |
ANS: A PTS: 1
- Which method of knowing is used in the following example? An individual accepts as true that black holes exist because 10 physics Nobel laureates assert such is the case.
a. | Method of Authority |
b. | Method of Intuition |
c. | Scientific Method |
d. | Rationalism |
ANS: A PTS: 1 MSC: WWW
- Which method of knowing is used in the following example? You have been struggling to determine the underlying explanation for the sadness you have been feeling for the past couple of months. Since you haven’t come up with the explanation, you give up on the struggle and decide to just go on with your life. Two days later, an explanation pops into your consciousness that you are convinced is correct.
a. | Method of Authority |
b. | Method of Intuition |
c. | Scientific Method |
d. | Rationalism |
ANS: B PTS: 1 MSC: WWW
- In acquiring knowledge the method that employs logic, reasoning and objective assessment is referred to as ____.
a. | the method of authority |
b. | intuition |
c. | rationalism |
d. | scientific method |
ANS: D PTS: 1 MSC: WWW
Exhibit 1-1
Let’s assume you are conducting an experiment to determine the effect of a new drug on the incidence of epileptic seizures. You select 20 epileptics from the 150 epileptics being treated at a nearby hospital and administer the drug to them. You record the number of seizures in each of the 20 subjects for one month.
- Refer to Exhibit 1-1. The new drug is an example of a(n) ____.
a. | dependent variable |
b. | constant |
c. | statistic |
d. | independent variable |
ANS: D PTS: 1
- Refer to Exhibit 1-1. Incidence of seizures is an example of a(n) ____.
a. | dependent variable |
b. | constant |
c. | statistic |
d. | independent variable |
ANS: A PTS: 1
- Refer to Exhibit 1-1. The 20 subjects constitute ____.
a. | the dependent variable |
b. | the sample |
c. | a statistic |
d. | the independent variable |
ANS: B PTS: 1
- Refer to Exhibit 1-1. The 150 epileptics constitute ____.
a. | the dependent variable |
b. | a parameter |
c. | a statistic |
d. | the independent variable |
ANS: B PTS: 1
- Refer to Exhibit 1-1. The number of seizures for each of the 20 subjects constitutes ____.
a. | the dependent variable |
b. | data |
c. | a statistic |
d. | the independent variable |
ANS: B PTS: 1
- Refer to Exhibit 1-1. Then you record the number of seizures in each of the 20 subjects for one month without the drug. Being compulsive, you also record the number of seizures for the remaining 130 epileptics for one month. The number of seizures for each of the 130 epileptics constitutes ____.
a. | the dependent variable |
b. | data |
c. | a statistic |
d. | independent variable |
ANS: B PTS: 1
- Refer to Exhibit 1-1. The average (mean) number of seizures for the 20 subjects is called ____.
a. | the dependent variable |
b. | data |
c. | a statistic |
d. | a parameter |
ANS: C PTS: 1
Exhibit 1-2
In order to estimate the average (mean) weight of all professional football players, an investigator determines the weight of the “Dallas Cowboy” players.
- Refer to Exhibit 1-2. Weight is an example of a(n) ____.
a. | independent variable |
b. | constant |
c. | statistic |
d. | dependent variable |
ANS: D PTS: 1
- Refer to Exhibit 1-2. The weight of each Dallas Cowboy is(are) called ____.
a. | constants |
b. | data |
c. | parameters |
d. | statistics |
ANS: B PTS: 1
- Refer to Exhibit 1-2. The Dallas Cowboys are a ____.
a. | population |
b. | parameter |
c. | sample |
d. | statistic |
ANS: C PTS: 1
- Refer to Exhibit 1-2. All professional football players constitute a ____.
a. | population |
b. | parameter |
c. | sample |
d. | statistic |
ANS: A PTS: 1
- Refer to Exhibit 1-2. The average (mean) weight of the Dallas Cowboys is called a ____.
a. | population |
b. | parameter |
c. | sample |
d. | statistic |
ANS: D PTS: 1
- Refer to Exhibit 1-2. The average (mean) weight of all professional football players is called a ____.
a. | population |
b. | parameter |
c. | sample |
d. | statistic |
ANS: B PTS: 1
Exhibit 1-3
In order to estimate the amount of TV watched by New York City adults, a sociologist surveys a random sample of adults from this city.
- Refer to Exhibit 1-3. The obtained raw scores are called ____.
a. | data |
b. | constants |
c. | statistics |
d. | populations |
ANS: A PTS: 1
- Refer to Exhibit 1-3. The average (mean) of the raw scores is a ____.
a. | population |
b. | sample |
c. | statistic |
d. | parameter |
ANS: C PTS: 1
- Refer to Exhibit 1-3. All of the New York City adults constitute a ____.
a. | population |
b. | sample |
c. | statistic |
d. | parameter |
ANS: A PTS: 1
Exhibit 1-4
In order to estimate the height of all students at your university, let’s assume you have measured the height of all psychology majors at the university.
- Refer to Exhibit 1-4. The resulting raw scores are called ____.
a. | constants |
b. | data |
c. | coefficients |
d. | statistics |
ANS: B PTS: 1
- Refer to Exhibit 1-4. The height scores of all psychology majors constitute a ____.
a. | population |
b. | sample |
c. | parameter |
d. | statistic |
ANS: B PTS: 1
- Refer to Exhibit 1-4. If you had measured the height scores of all students at your university, these scores would constitute a ____.
a. | population |
b. | sample |
c. | parameter |
d. | statistic |
ANS: A PTS: 1
- Refer to Exhibit 1-4. If you had measured the height scores of all students at your university, the average (mean) of these scores would constitute a ____.
a. | population |
b. | sample |
c. | parameter |
d. | statistic |
ANS: C PTS: 1
- Refer to Exhibit 1-4. The average (mean) value of the measured height scores constitutes a ____.
a. | population |
b. | sample |
c. | parameter |
d. | statistic |
ANS: D PTS: 1
Exhibit 1-5
In order to estimate the attention level of college undergraduates in the United States, a psychologist measures the attention span of the undergraduates at a local university.
- Refer to Exhibit 1-5. The mean of these scores is a ____.
a. | parameter |
b. | population |
c. | statistic |
d. | sample |
ANS: C PTS: 1
- Refer to Exhibit 1-5. The undergraduates at the local university are a ____.
a. | parameter |
b. | population |
c. | sample |
d. | statistic |
ANS: C PTS: 1
Exhibit 1-6
In order to estimate the ratio of white to black students in his college, a professor determines the proportion of whites and blacks in his class.
- Refer to Exhibit 1-6. The resulting proportion is called a ____.
a. | population |
b. | sample |
c. | parameter |
d. | statistic |
ANS: D PTS: 1
- Refer to Exhibit 1-6. The students in the professor’s class are called a ____.
a. | sample |
b. | population |
c. | statistic |
d. | parameter |
ANS: A PTS: 1
- Refer to Exhibit 1-6. The students of the entire college are called a ____.
a. | sample |
b. | population |
c. | statistic |
d. | parameter |
ANS: B PTS: 1
- Inferential statistics ____.
a. | is the same as descriptive statistics |
b. | also uses methods of descriptive statistics |
c. | allows one to make inferences about a sample based on population data |
d. | allows one to make inferences about a population based on sample data |
e. | b and d |
ANS: E PTS: 1
- Descriptive statistics are used to ____.
a. | calculate the mean and standard deviation of a sample |
b. | calculate the mean and standard deviation of a population |
c. | graph a distribution of raw scores |
d. | b and c |
e. | a, b and c |
ANS: E PTS: 1 MSC: WWW
- In the equation Y = bX + a, b is a(n) ____.
a. | independent variable |
b. | dependent variable |
c. | constant |
d. | coefficient |
e. | c and d |
ANS: E PTS: 1
- When one analyzes data based on a sample, one calculates a ____.
a. | parameter |
b. | variable |
c. | constant |
d. | statistic |
ANS: D PTS: 1 MSC: WWW
- Mathematical methods used to draw tentative conclusions about a population based on sample data are referred to as ____.
a. | descriptive statistics |
b. | sample statistics |
c. | inferential statistics |
d. | random sampling |
e. | magic |
ANS: C PTS: 1 MSC: WWW
- The variable that the experimenter manipulates is called the ____.
a. | independent variable |
b. | dependent variable |
c. | constant variable |
d. | experimental variable |
ANS: A PTS: 1
- From which of the following studies can one most reasonably determine cause and effect?
a. | correlational study |
b. | true experiment |
c. | naturalistic observation |
d. | all of the above equally well |
ANS: B PTS: 1 MSC: WWW
- In inferential statistics the object is usually to generalize from a ____ to a ____.
a. | data; variable |
b. | sample; population |
c. | population; sample |
d. | constant; variable |
ANS: B PTS: 1 MSC: WWW
- For a list of sample data the lowest and highest score values are examples of ____ statistics.
a. | inferential |
b. | sample |
c. | population |
d. | descriptive |
ANS: D PTS: 1 MSC: WWW
- To avoid unknown, systematic factors that may bias the results of an experiment, the experimenter should select a ____ sample from a population and use controlled conditions.
a. | wise |
b. | small |
c. | random |
d. | single |
ANS: C PTS: 1
- Descriptive statistics are helpful in ____ and ____ raw data.
a. | generalizing; inferring |
b. | organizing; tenderizing |
c. | confusing; confounding |
d. | summarizing; characterizing |
ANS: D PTS: 1 MSC: WWW
- This question has been omitted from the ExamView test bank. To maintain the integrity of the numbering system between the printed copy and ExamView, this question has been marked “do not use on test” in ExamView’s question information dialog.
a. | not available |
b. | not available |
c. | not available |
d. | not available |
ANS: A PTS: 1
- Pick the best answer from the following statements.
a. | The measurements that are made on the subjects of an experiment are called data. |
b. | A statistic is a number calculated on sample data that quantifies a characteristic of the sample. |
c. | A parameter is a number calculated on population data that quantifies a characteristic of the population. |
d. | All of the above statements are true. |
ANS: D PTS: 1
- A statistic is defined as ____.
a. | the score on the dependent variable of a particular subject in the sample |
b. | a number calculated on population data that quantifies a characteristic of the population |
c. | a number calculated on sample data that quantifies a characteristic of the sample |
d. | the number of subjects in the sample |
ANS: C PTS: 1
- A parameter is defined as ____.
a. | the score on the dependent variable of a particular subject in the population |
b. | a number calculated on population data that quantifies a characteristic of the population |
c. | a number calculated on sample data that quantifies a characteristic of the sample |
d. | the number of individuals in the population |
ANS: B PTS: 1
- Data is defined as ____.
a. | the measurements that are made on the subjects of an experiment |
b. | the score on the dependent variable of a particular subject in the sample |
c. | the score on the dependent variable of a particular subject in the population |
d. | the number of individuals in the sample |
ANS: A PTS: 1
- A sample is defined as ____.
a. | the subjects in an experiment |
b. | the complete set of individuals, objects, or scores that the investigator is interested in studying |
c. | a subset of the population |
d. | a and c |
e. | a and b |
ANS: D PTS: 1
- A population is defined as ____.
a. | the complete set of individuals living in Seattle in a study interested in the complete set of individuals living in the US. |
b. | the complete set of individuals the investigator wishes to generalize to from an experiment. |
c. | the complete set of individuals, objects, or scores that the investigator is interested in studying |
d. | a and c |
e. | b and c |
ANS: E PTS: 1
- The independent variable in an experiment is defined or identified as ____.
a. | “IQ”, in an experiment studying the effect of early education on IQ. |
b. | the variable that is systematically manipulated by the experimenter |
c. | the variable the experimenter measures to determine if there is a real effect |
d. | “Early Education”, in an experiment studying the effect of Early Education on IQ |
e. | b and d |
ANS: E PTS: 1
- The dependent variable in an experiment is defined or identified as ____.
a. | the variable the experimenter measures to determine if there is a real effect |
b. | the variable that is systematically manipulated by the experimenter |
c. | “IQ”, in an experiment studying the effect of Early Education on IQ |
d. | “Early Education”, in an experiment studying the effect of Early education on IQ |
e. | a and c |
f. | a and d |
ANS: E PTS: 1 MSC: WWW
- A variable is defined or identified as ____.
a. | “Early Education”, in an experiment studying the effect of Early Education on IQ |
b. | a characteristic of some event, object or person that has the same value regardless of differing times or conditions. |
c. | a characteristic of some event, object, or person that may have different values at different times depending on the conditions. |
d. | “IQ”, in an experiment studying the effect of Early Education on IQ |
e. | a and d |
f. | a, c, and d |
ANS: F PTS: 1
TRUE/FALSE
- A sample is a subset of a population.
ANS: T PTS: 1
- The dependent variable is the variable that is systematically manipulated.
ANS: F PTS: 1
- The independent variable is the variable that is measured to determine the effect of the independent variable.
ANS: F PTS: 1
- A statistic is to a sample as a parameter is to a population.
ANS: T PTS: 1 MSC: WWW
- Descriptive statistics involves characterizing the obtained data.
ANS: T PTS: 1
- Inferential statistics uses the sample data to generalize to populations.
ANS: T PTS: 1
- Observational studies involve the manipulation of variables by the investigator.
ANS: F PTS: 1 MSC: WWW
- True experiments involve the manipulation of variables by the investigator.
ANS: T PTS: 1
- Observational studies involve the use of independent variables.
ANS: F PTS: 1
- The method of authority is opposed to the scientific method.
ANS: T PTS: 1
- Intuition is often used as part of the scientific method.
ANS: T PTS: 1
- Data are an indispensable part of the scientific method.
ANS: T PTS: 1 MSC: WWW
- The only value of random sampling is to achieve a representative sample.
ANS: F PTS: 1 MSC: WWW
- One is able to determine cause and effect from observational studies.
ANS: F PTS: 1
- In an experiment conducted to determine the effect of testosterone on aggression, testosterone is the independent variable.
ANS: F PTS: 1
- Statistical methods that use sample data to make statements about populations are called inferential statistics.
ANS: T PTS: 1
- The goal of descriptive statistics is solely to summarize and organize data.
ANS: F PTS: 1 MSC: WWW
- In order to determine cause and effect, a researcher needs to do a true experiment.
ANS: T PTS: 1 MSC: WWW
DEFINITIONS
- Define parameter.
ANS:
Answer not provided.
PTS: 1
- Define statistic.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Define dependent variable.
ANS:
Answer not provided.
PTS: 1
- Define independent variable.
ANS:
Answer not provided.
PTS: 1
- Define data.
ANS:
Answer not provided.
PTS: 1
- Define descriptive statistics.
ANS:
Answer not provided.
PTS: 1
- Define inferential statistics.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
SHORT ANSWER
- A developmental psychologist conducts an experiment to determine if exposure to an enriched environment shortly after birth will cause increased brain development. Twenty two-month-old rats are randomly selected from a pool of one thousand two-month-old rat pups. Ten of the twenty pups are exposed to an enriched environment for three weeks and the other ten to the usual environment for the same period of time. At a suitable time after the exposure, the psychologist measures the number of neurons per cm^{3} in the brain of each rat. A comparison is then made of the mean number of neurons per cm^{3} for each group. Identify the following:
a. | The population |
b. | The sample |
c. | The independent variable |
d. | The dependent variable |
e. | Any statistics |
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Compare the method of authority with the scientific method.
ANS:
Answer not provided.
PTS: 1
- What is the major difference between descriptive and inferential statistics? Illustrate, using an example.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Compare intuition and scientific method as methods of knowing.
ANS:
Answer not provided.
PTS: 1
- How does natural observation research differ from true experiments?
ANS:
Answer not provided.
PTS: 1
- A scientist asserts that properly collected data are essential to the scientific method. Is she correct? Explain.
ANS:
Answer not provided.
PTS: 1
Chapter 2—Basic Mathematical and Measurement Concepts
MULTIPLE CHOICE
- Given the following subjects and scores, which symbol would be used to represent the score of 3?
Subject | 1 | 2 | 3 | 4 | 5 |
Score | 12 | 21 | 8 | 3 | 30 |
a. | X_{8} |
b. | X_{4} |
c. | X_{3} |
d. | X_{2} |
ANS: B PTS: 1 MSC: WWW
- We have collected the following data:
X_{1} = 6, X_{2} = 2, X_{3} = 4, X_{4} = 1, X_{5} = 3
For these data, is equal to ____.
a. | 16 |
b. | 10 |
c. | 7 |
d. | 13 |
ANS: D PTS: 1 MSC: WWW
- Reaction time in seconds is an example of a(n) ____ scale.
a. | ratio |
b. | ordinal |
c. | interval |
d. | nominal |
ANS: A PTS: 1
- After performing several clever calculations on your calculator, the display shows the answer 53.655001. What is the appropriate value rounded to two decimal places?
a. | 53.65 |
b. | 53.66 |
c. | 53.64 |
d. | 53.60 |
ANS: B PTS: 1
- Consider the following points on a scale:
If the scale upon which A, B, C, and D are arranged is a nominal scale, we can say ____.
a. | B = 2A |
b. | B – A = D – C |
c. | both a and b |
d. | neither a nor b |
ANS: D PTS: 1
- When rounded to two decimal places, the number 3.175000 becomes ____.
a. | 3.17 |
b. | 3.20 |
c. | 3.18 |
d. | 3.10 |
ANS: C PTS: 1 MSC: WWW
Exhibit 2-1
Given the following data:
X_{1} = 1, X_{2} = 4, X_{3} = 5, X_{4} = 8, X_{5} = 10
- Refer to Exhibit 2-1. Evaluate S X.
a. | 1 |
b. | 18 |
c. | 27 |
d. | 28 |
ANS: D PTS: 1
- Refer to Exhibit 2-1. Evaluate S X^{2}.
a. | 56 |
b. | 784 |
c. | 206 |
d. | 28 |
ANS: C PTS: 1
- Refer to Exhibit 2-1. Evaluate (S X)^{2}.
a. | 56 |
b. | 784 |
c. | 206 |
d. | 28 |
ANS: B PTS: 1
- Refer to Exhibit 2-1. Evaluate .
a. | 17 |
b. | 27 |
c. | 28 |
d. | 23 |
ANS: A PTS: 1
- Refer to Exhibit 2-1. Evaluate .
a. | 53 |
b. | 47 |
c. | 48 |
d. | 32 |
ANS: D PTS: 1
- Refer to Exhibit 2-1. Evaluate .
a. | 47 |
b. | 53 |
c. | 48 |
d. | 32 |
ANS: A PTS: 1
- A discrete scale of measurement ____.
a. | is the same as a continuous scale |
b. | provides exact measurements |
c. | necessarily uses whole numbers |
d. | b and c |
ANS: B PTS: 1
- Consider the following points on a scale:
If the scale upon which A, B, C, and D are arranged is an interval scale, we can say ____.
a. | B = 2A |
b. | B – A = D – C |
c. | both a and b |
d. | neither a nor b |
ANS: B PTS: 1 MSC: WWW
- The number 83.476499 rounded to three decimal places is ____.
a. | 83.477 |
b. | 83.480 |
c. | 83.476 |
d. | 83.470 |
ANS: C PTS: 1
- The number 99.44650 rounded to two decimal places is ____.
a. | 99.45 |
b. | 99.46 |
c. | 99.44 |
d. | 99.40 |
ANS: A PTS: 1
- “Brand of soft drink” is measured on a(n) ____.
a. | nominal scale |
b. | ordinal scale |
c. | interval scale |
d. | ratio scale |
ANS: A PTS: 1
- At the annual sailing regatta, prizes are awarded for 1st, 2nd, 3rd, 4th, and 5th place. These “places” comprise a(n) ____.
a. | nominal scale |
b. | ordinal scale |
c. | interval scale |
d. | ratio scale |
ANS: B PTS: 1
- Which of the following numbers is rounded incorrectly to two decimal places?
a. | 10.47634 ® 10.48 |
b. | 15.36485 ® 15.36 |
c. | 21.47500 ® 21.47 |
d. | 8.24501 ® 8.25 |
e. | 6.66500 ® 6.66 |
ANS: C PTS: 1
- Consider the following points on a scale:
If the scale upon which points A, B, C, and D are shown is an ordinal scale, we can meaningfully say ____.
a. | B – A < D – C |
b. | B < C/2 |
c. | B = 2A |
d. | C > B |
ANS: D PTS: 1
- A continuous scale of measurement is different than a discrete scale in that a continuous scale ____.
a. | is an interval scale, not a ratio scale |
b. | never provides exact measurements |
c. | can take an infinite number of intermediate possible values |
d. | never uses decimal numbers |
e. | b and c |
ANS: E PTS: 1
- Sex of children is an example of a(n) ____ scale.
a. | ratio |
b. | nominal |
c. | ordinal |
d. | interval |
ANS: B PTS: 1
- Which of the following variables has been labeled with an incorrect measuring scale?
a. | the number of students in a psychology class – ratio |
b. | ranking in a beauty contest – ordinal |
c. | finishing order in a poetry contest – ordinal |
d. | self-rating of anxiety level by students in a statistics class – ratio |
ANS: D PTS: 1
- A nutritionist uses a scale that measures weight to the nearest 0.01 grams. A slice of cheese weighs 0.35 grams on the scale. The variable being measured is a ____.
a. | discrete variable |
b. | constant |
c. | continuous variable |
d. | random variable |
ANS: C PTS: 1
- A nutritionist uses a scale that measures weight to the nearest 0.01 grams. A slice of cheese weighs 0.35 grams on the scale. The true weight of the cheese ____.
a. | is 0.35 grams |
b. | may be anywhere in the range 0.345-0.355 grams |
c. | may be anywhere in the range 0.34-0.35 grams |
d. | may be anywhere in the range 0.34-0.36 grams |
ANS: B PTS: 1
- In a 10-mile cross-country race, all runners are randomly assigned an identification number. These numbers represent a(n) ____.
a. | nominal scale |
b. | ratio scale |
c. | interval scale |
d. | ordinal scale |
ANS: A PTS: 1
- In a 10-mile cross-country race, a comparison of each runner’s finishing time would represent a(n) ____.
a. | nominal scale |
b. | ratio scale |
c. | interval scale |
d. | ordinal scale |
ANS: B PTS: 1
- The sum of a distribution of 40 scores is 150. If we add a constant of 5 to each score, the resulting sum will be ____.
a. | 158 |
b. | 350 |
c. | 150 |
d. | 195 |
ANS: B PTS: 1
Exhibit 2-2
Given the following set of numbers:
X_{1} = 2, X_{2} = 4, X_{3} = 6, X_{4} = 10
- Refer to Exhibit 2-2. What is the value for S X?
a. | 12 |
b. | 156 |
c. | 480 |
d. | 22 |
ANS: D PTS: 1
- Refer to Exhibit 2-2. What is the value of S X^{2}?
a. | 156 |
b. | 22 |
c. | 480 |
d. | 37 |
ANS: A PTS: 1 MSC: WWW
- Refer to Exhibit 2-2. What is the value of X_{4}^{2}?
a. | 4 |
b. | 6 |
c. | 100 |
d. | 10 |
ANS: C PTS: 1
- Refer to Exhibit 2-2. What is the value of (S X)^{2}?
a. | 480 |
b. | 484 |
c. | 156 |
d. | 44 |
ANS: B PTS: 1
- Refer to Exhibit 2-2. What is the value of N?
a. | 2 |
b. | 4 |
c. | 6 |
d. | 10 |
ANS: B PTS: 1
- Refer to Exhibit 2-2. What is the value of (S X)/N?
a. | 5 |
b. | 4 |
c. | 6 |
d. | 5.5 |
ANS: D PTS: 1
- Classifying subjects on the basis of sex is an example of using what kind of scale?
a. | nominal |
b. | ordinal |
c. | interval |
d. | ratio |
e. | bathroom |
ANS: A PTS: 1 MSC: WWW
- Number of bar presses is an example of a(n) ____ variable.
a. | discrete |
b. | continuous |
c. | nominal |
d. | ordinal |
ANS: A PTS: 1
- Using an ordinal scale to assess leadership, which of the following statements is appropriate?
a. | A has twice as much leadership ability as B |
b. | X has no leadership ability |
c. | Y has the most leadership ability |
d. | all of the above |
ANS: C PTS: 1
- The number of legs on a centipede is an example of a(n) ____ scale.
a. | nominal |
b. | ordinal |
c. | ratio |
d. | continuous |
ANS: C PTS: 1
- What are the real limits of the observation of 6.1 seconds (measured to the nearest second)?
a. | 6.05–6.15 |
b. | 5.5–6.5 |
c. | 6.0–6.2 |
d. | 6.00–6.20 |
ANS: A PTS: 1 MSC: WWW
- What is 17.295 rounded to one decimal place?
a. | 17.1 |
b. | 17.0 |
c. | 17.2 |
d. | 17. |
ANS: D PTS: 1
- What is the value of 0.05 rounded to one decimal place?
a. | 0.0 |
b. | 0.1 |
c. | 0.2 |
d. | 0.5 |
ANS: A PTS: 1
- The symbol “S” means:
a. | add the scores |
b. | summarize the data |
c. | square the value |
d. | multiply the scores |
ANS: A PTS: 1
- A therapist measures the difference between two clients. If the therapist can say that Rebecca’s score is higher than Sarah’s, but can’t specify how much higher, the measuring scale used must have been a(n) ____ scale.
a. | nominal |
b. | ordinal |
c. | interval |
d. | ratio |
ANS: B PTS: 1 MSC: WWW
- An individual is measuring various objects. If the measurements made are to determine into which of six categories each object belongs, the measuring scale used must have been a(n)____ scale.
a. | nominal |
b. | ordinal |
c. | interval |
d. | ratio |
ANS: A PTS: 1 MSC: WWW
- If an investigator determines that Carlo’s score is five times as large as the score of Juan, the measuring scale used must have been a(n) ____ scale.
a. | nominal |
b. | ordinal |
c. | interval |
d. | ratio |
ANS: D PTS: 1 MSC: WWW
The following problem(s) are for your own use in evaluating your skills at elementary algebra. If you do not get all the problem(s) correct you should probably review your algebra.
- Where 3X = 9, what is the value of X?
a. | 3 |
b. | 6 |
c. | 9 |
d. | 12 |
ANS: A PTS: 1
- For X + Y = Z, X equals ____.
a. | Y + Z |
b. | Z – Y |
c. | Z/Y |
d. | Y/Z |
ANS: B PTS: 1
- 1/X + 2/X equals ____.
a. | 2/X |
b. | 3/2X |
c. | 3/X |
d. | 2/X^{2} |
ANS: C PTS: 1
- What is (4 – 2)(3×4)/(6/3)?
a. | 24 |
b. | 1.3 |
c. | 12 |
d. | 6 |
ANS: C PTS: 1
- 6 + 4´3 – 1 simplified is ____.
a. | 29 |
b. | 48 |
c. | 71 |
d. | 17 |
ANS: D PTS: 1
- X = Y/Z can be expressed as ____.
a. | Y = (Z)(X) |
b. | X = Z/Y |
c. | Y = X/Z |
d. | Z = X + Y |
ANS: A PTS: 1
- 2^{4} equals ____.
a. | 4 |
b. | 32 |
c. | 8 |
d. | 16 |
ANS: D PTS: 1
- equals ____.
a. | ±3 |
b. | ±81 |
c. | ±9 |
d. | ±27 |
ANS: C PTS: 1
- X(Z + Y) equals ____.
a. | XZ + Y |
b. | ZX + YX |
c. | (X)(Y)(Z) |
d. | (Z + Y)/X |
ANS: B PTS: 1
- 1/2 + 1/4 equals ____.
a. | 1/6 |
b. | 1/8 |
c. | 2/8 |
d. | 3/4 |
ANS: D PTS: 1
- X^{6}/X^{2} equals ____.
a. | X^{8} |
b. | X^{4} |
c. | X^{2} |
d. | X^{3} |
ANS: B PTS: 1
TRUE/FALSE
- When doing summation, the number above the summation sign indicates the term ending the summation and the number below indicates the beginning term.
ANS: T PTS: 1 MSC: WWW
- S X^{2} and (S X)^{2} generally yield the same answer.
ANS: F PTS: 1 MSC: WWW
- With nominal scales there is a numerical relationship between the units of the scale.
ANS: F PTS: 1
- If IQ was measured on a ratio scale, and John had an IQ of 40 and Fred an IQ of 80, it would be correct to say that Fred was twice as intelligent as John.
ANS: T PTS: 1
- An ordinal scale possesses the attributes of magnitude and equal interval.
ANS: F PTS: 1
- Most scales used for measuring psychological variables are either ratio or interval.
ANS: F PTS: 1
- Measurement is always approximate with a continuous variable.
ANS: T PTS: 1 MSC: WWW
- It is standard practice to carry all intermediate calculations to four more decimal places than will be reported in the final answer.
ANS: F PTS: 1
- In rounding, if the remainder beyond the last digit is greater than 1/2, add one to the last digit. If the remainder is less than 1/2, leave the last digit as it is.
ANS: T PTS: 1
- It is legitimate to do ratios with interval scaling.
ANS: F PTS: 1
- The number of students in a class is an example of a continuous variable.
ANS: F PTS: 1
- The real limits of a discrete variable are those values that are above and below the recorded value by one half of the smallest measuring unit of the scale.
ANS: F PTS: 1
- When rounding, if the decimal remainder is equal to 1/2 and the last digit of the answer is even, add 1 to the last digit of the answer.
ANS: F PTS: 1
- A fundamental property of a nominal scale is equivalence.
ANS: T PTS: 1
- An interval scale is like a ratio scale, except that the interval scale doesn’t possess an absolute zero point.
ANS: T PTS: 1
- A discrete variable requires nominal or interval scaling.
ANS: T PTS: 1 MSC: WWW
- Classifying students into whether they are good, fair, or poor speakers is an example of ordinal scaling.
ANS: T PTS: 1
- Determining the number of students in each section of introductory psychology involves the use of a ratio scale.
ANS: T PTS: 1 MSC: WWW
- In a race, Sam came in first and Fred second. Determining the difference in time to complete the race between Sam and Fred involves an ordinal scale
ANS: F PTS: 1
- If the remainder of a number = 1/2, we always round the last digit up.
ANS: F PTS: 1
DEFINITIONS
- Define continuous variable.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Define discrete variable.
ANS:
Answer not provided.
PTS: 1
- Define interval scale.
ANS:
Answer not provided.
PTS: 1
- Define nominal scale.
ANS:
Answer not provided.
PTS: 1
- Define ratio scale.
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- Define real limits of a continuous variable.
ANS:
Answer not provided.
PTS: 1
SHORT ANSWER
- How does an interval scale differ from an ordinal scale?
ANS:
Answer not provided.
PTS: 1
- Give two differences between continuous and discrete scales.
ANS:
Answer not provided.
PTS: 1
- What are the four types of scales and what mathematical operations can be done with each?
ANS:
Answer not provided.
PTS: 1
- Prove algebraically that .
ANS:
Answer not provided.
PTS: 1
- What is a discrete variable? Give an example.
ANS:
Answer not provided.
PTS: 1
- Student A claims that because his IQ is twice that of Student B, he is twice as smart as Student B. Is student A correct? Explain.
ANS:
Answer not provided.
PTS: 1
- What is meant by “the real limits of a continuous variable.”
ANS:
Answer not provided.
PTS: 1 MSC: WWW
- The faculty of a psychology department are trying to decide between three candidates for a single faculty position. The department chairperson suggests that to decide, each faculty person should rank order the candidates from 1 to 3, and the ranks would then be averaged. The candidate with the highest average would be offered the position. Mathematically, what is wrong with that proposal?
ANS:
Answer not provided.
PTS: 1 MSC: WWW
Chapter 5—The Normal Curve and Standard Scores
MULTIPLE CHOICE
Exhibit 5-1
A stockbroker has kept a daily record of the value of a particular stock over the years and finds that prices of the stock form a normal distribution with a mean of $8.52 with a standard deviation of $2.38.
- Refer to Exhibit 5-1. The percentile rank of a price of $13.87 is ____.
a. | 48.78% |
b. | 1.22% |
c. | 98.78% |
d. | 51.22% |
- Refer to Exhibit 5-1. What percentage of the distribution lies between $5 and $11?
a. | 21.48% |
b. | 78.41% |
c. | 49.41% |
d. | 57.98% |
- Refer to Exhibit 5-1. What percentage of the distribution lies below $7.42?
a. | 17.72% |
b. | 32.28% |
c. | 82.28% |
d. | 31.92% |
- Refer to Exhibit 5-1. The stock price beyond which 0.05 of the distribution falls is ____.
a. | $ 4.60 |
b. | $12.47 |
c. | $ 4.57 |
d. | $12.44 |
- Refer to Exhibit 5-1. The percentage of scores that lie between $9.00 and $10.00 is ____.
a. | 15.31% |
b. | 31.17% |
c. | 23.24% |
d. | 7.93% |
Exhibit 5-2
A testing bureau reports that the mean for the population of Graduate Record Exam (GRE) scores is 500 with a standard deviation of 90. The scores are normally distributed.
- Refer to Exhibit 5-2. The percentile rank of a score of 667 is ____.
a. | 3.14% |
b. | 96.78% |
c. | 3.22% |
d. | 96.86% |
- Refer to Exhibit 5-2. The proportion of scores that lie above 650 is ____.
a. | 0.4535 |
b. | 0.9535 |
c. | 0.0475 |
d. | 0.0485 |
- Refer to Exhibit 5-2. The proportion of scores that lie between 460 and 600 is ____.
a. | 0.4394 |
b. | 0.5365 |
c. | 0.4406 |
d. | 0.4635 |
- Refer to Exhibit 5-2. The raw score that lies at the 90th percentile is ____.
a. | 615.20 |
b. | 384.80 |
c. | 616.10 |
d. | 383.90 |
- Refer to Exhibit 5-2. The proportion of scores between 300 and 400 is ____.
a. | 0.3665 |
b. | 0.4868 |
c. | 0.8533 |
d. | 0.1203 |
- The standard deviation of the z distribution equals ____.
a. | 1 |
b. | 0 |
c. | S X |
d. | N |
- The mean of the z distribution equals ____.
a. | 1 |
b. | 0 |
c. | S X |
d. | N |
- The z score corresponding to the mean of a raw score distribution equals ____.
a. | the mean of the raw scores |
b. | 0 |
c. | 1 |
d. | N |
- The normal curve is ____.
a. | linear |
b. | rectangular |
c. | bell-shaped |
d. | skewed |
- In a normal curve, the inflection points occur at ____.
a. | m ± 1s |
b. | ±1s |
c. | m ± 2s |
d. | m |
- The z score corresponding to a raw score of 120 is ____.
a. | 1.2 |
b. | 2.0 |
c. | 1.0 |
d. | impossible to compute from the information given |
Exhibit 5-3
An economics test was given and the following sample scores were recorded:
Individual | A | B | C | D | E | F | G | H | I | J |
Score | 12 | 12 | 7 | 10 | 9 | 12 | 13 | 8 | 9 | 8 |
- Refer to Exhibit 5-3. The mean of the distribution is ____.
a. | 12.00 |
b. | 10.00 |
c. | 9.00 |
d. | 8.00 |
- Refer to Exhibit 5-3. The standard deviation of the distribution is ____.
a. | 10.20 |
b. | 2.10 |
c. | 2.11 |
d. | 10.74 |
- Refer to Exhibit 5-3. The z score for individual D is ____.
a. | 1 |
b. | 0 |
c. | 10 |
d. |
- Refer to Exhibit 5-3. The z score for individual E is ____.
a. | 0.47 |
b. | 9.00 |
c. | 4.27 |
d. | -0.47 |
- Refer to Exhibit 5-3. The z score for individual G is ____.
a. | -1.42 |
b. | 13.00 |
c. | 1.42 |
d. | 6.16 |
Exhibit 5-4
A distribution has a mean of 60.0 and a standard deviation of 4.3.
- Refer to Exhibit 5-4. The raw score corresponding to a z score of 0.00 is ____.
a. | 64.3 |
b. | 14.0 |
c. | 4.3 |
d. | 60.0 |
- Refer to Exhibit 5-4. The raw score corresponding to a z score of -1.51 is ____.
a. | 53.5 |
b. | 66.5 |
c. | 66.4 |
d. | 53.6 |
- Refer to Exhibit 5-4. The raw score corresponding to a z score of 2.02 is ____.
a. | 51.3 |
b. | 68.7 |
c. | 51.4 |
d. | 68.6 |
- If a population of scores is normally distributed, has a mean of 45 and a standard deviation of 6, the most extreme 5% of the scores lie beyond the score(s) of ____.
a. | 35.13 |
b. | 45.99 |
c. | 56.76 and 33.24 |
d. | 45.99 and 35.13 |
- If a distribution of raw scores is negatively skewed, transforming the raw scores into z scores will result in a ____ distribution.
a. | normal |
b. | bell-shaped |
c. | positively skewed |
d. | negatively skewed |
- The mean of the z distribution equals ____.
a. | 0 |
b. | 1 |
c. | N |
d. | depends on the raw scores |
- The standard deviation of the z distribution equals ____.
a. | 0 |
b. | 1 |
c. | the variance of the z distribution |
d. | b and c |
- S(z – m_{z}) equals ____.
a. | 0 |
b. | 1 |
c. | the variance |
d. | cannot be determined |
- The proportion of scores less than z = 0.00 is ____.
a. | 0.00 |
b. | 0.50 |
c. | 1.00 |
d. | -0.50 |
- In a normal distribution the z score for the mean equals ____.
a. | 0 |
b. | the z score for the median |
c. | the z score for the mode |
d. | all of the above |
- In a normal distribution approximately ____ of the scores will fall within 1 standard deviation of the mean.
a. | 14% |
b. | 95% |
c. | 70% |
d. | 83% |
- Would you rather have an income (assume a normal distribution and you are greedy) ____?
a. | with a z score of 1.96 |
b. | in the 95th percentile |
c. | with a z score of -2.00 |
d. | with a z score of 0.000 |
- How much would your income be if its z score value was 2.58?
a. | $10,000 |
b. | $ 9,999 |
c. | $ 5,000 |
d. | cannot be determined from information given |
- Which of the following z scores represent(s) the most extreme value in a distribution of scores assuming they are normally distributed?
a. | 1.96 |
b. | 0.0001 |
c. | -0.0002 |
d. | -3.12 |
- Assuming the z scores are normally distributed, what is the percentile rank of a z score of -0.47?
a. | 31.92 |
b. | 18.08 |
c. | 50.00 |
d. | 47.00 |
e. | 0.06 |
- A standardized test has a mean of 88 and a standard deviation of 12. What is the score at the 90th percentile? Assume a normal distribution.
a. | 90.00 |
b. | 112.00 |
c. | 103.36 |
d. | 91.00 |
- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what is the percentile rank of a score of 56?
a. | 58.30 |
b. | 0.00 |
c. | 25.27 |
d. | 38.30 |
e. | 11.70 |
- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall below a score of 83.8?
a. | 55.00 |
b. | 79.12 |
c. | 20.88 |
d. | 29.12 |
e. | 70.88 |
- On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall between 70 and 80?
a. | 75.66 |
b. | 70 23 |
c. | 24.34 |
d. | 23.57 |
e. | 12.17 |
- You have just received your psychology exam grade and you did better than the mean of the exam scores. If so, the z transformed value of your grade must
a. | be greater than 1.00 |
b. | be greater than 0.00 |
c. | have a percentile rank greater than 50% |
d. | can’t determine with information given |
e. | b and c. |
- You have just taken a standardized skills test designed to help you make a career choice. Your math skills score was 63 and your writing skills score was 45. The standardized math distribution is normally distributed, with m = 50, and s = 8. The writing skills score distribution is also normally distributed, with m = 30, and s = 10. Based on this information, as between pursuing a career that requires good math skills or one requiring good writing skills, you should chose
a. | neither, your skills are below average in both |
b. | the career requiring good math skills. |
c. | neither, this approach is bogus; dream interpretation should be used instead. |
d. | the career requiring good writing skills. |
- A distribution of raw scores is positively skewed. You want to transform it so that it is normally distributed. Your friend, who fancies herself a statistics whiz, advises you to transform the raw scores to z scores; that the z scores will be normally distributed. You should
a. | Ignore the advice because your friend flunked her last statistics test |
b. | Ignore the advice because z distributions have the same shape as the raw scores. |
c. | Take the advice because z distributions are always normally distributed |
d. | Take the advice because z distributions are usually normally distributed |
- All bell-shaped curves
a. | are normal curves |
b. | have means = 0 |
c. | are symmetrical |
d. | a and c |
- If you transformed a set of raw scores, and then added 15 to each z score, the resulting scores
a. | would have a standard deviation = 1 |
b. | would have a mean = 0 |
c. | would have a mean =15 |
d. | would have a standard deviation > 1 |
e. | a and c |
- A set of raw scores has a rectangular shape. The z transformed scores for this set of raw scores has a ____ shape.
a. | rectangular |
b. | normal (bell-shaped) |
c. | it depends on the number of scores in the distribution |
d. | none of the above |
- Makaela took a Spanish exam; her grade was 79. The distribution was normally shaped with = 70 and s = 12. Juan took a History exam; his grade was 86. The distribution was normally shaped with = 80 and s = 8. Which did better on their exam relative to those taking the exam?
a. | Makaela. |
b. | Juan. |
c. | Neither, they both did as well as each other. |
d. | Makaela, because her exam was harder |
e. | a and d. |
- Table A (Areas under the normal curve) in your textbook has no negative z values, this means ____.
a. | the table can only be used with positive z values |
b. | the table can be used with both positive and negative z values because it is symmetrical |
c. | the table can be used with both positive and negative z values because it is skewed |
d. | none of the above |
- A testing service has 1000 raw scores. It wants to transform the distribution so that the mean = 10 and the standard deviation = 1. To do so, ____.
a. | Do a z transformation for each raw score and add 10 to each z score. |
b. | Do a z transformation for each raw score and multiply each by 10 |
c. | Divide the raw scores by 10 |
d. | Compute the deviation score for each raw score. Divide each deviation score by the standard deviation of the raw scores. Take this result for all scores and add 10 to each one. |
e. | a and d |
- Given the following set of sample raw scores, X: 1, 3, 4, 6, 8. What is the z transformed value for the raw score of 3?
a. | -0.18 |
b. | -0.48 |
c. | -0.15 |
d. | -0.52 |
TRUE/FALSE
- A z distribution always is normally shaped.
- All standard scores are z scores.
- A z score is a transformed score.
- A z score designates how many standard deviations the raw score is above or below the mean.
- The z distribution takes on the same shape as the raw scores.
- z scores allow comparison of variables that are measured on different scales.
- In a normal curve, the area contained between the mean and a score that is 2.30 standard deviations above the mean is 0.4893 of the total area.
- The normal curve reaches the horizontal axis in 4 standard deviations above and below the mean.
- For any z distribution of normally distributed scores, P_{50} is always equal to zero.
- If the original raw score distribution has a mean that is not equal to zero, the mean of the z transformed scores will not equal zero either.
- It is impossible to have a z score of 30.2.
- The area under the normal curve represents the proportion of scores that are contained in the area.
- If the raw score distribution is very positively skewed, the standard deviation of the z transformed scores will not equal 1.
- The area beyond a z score of -1.12 is the same as the area beyond a z score of 1.12.
- A raw score that is 1 standard deviation above the mean of the raw score distribution will have a z score of 1.
DEFINITIONS
- Define asymptotic.
- Define normal curve.
- Define standard (z) scores.
SHORT ANSWER
- List three characteristics of a z distribution.
- Is a z distribution always normally shaped? Explain.
- Does the z transformation result in a score having the same units of measurement as the raw score? Explain. Why is this advantageous?
- Are all bell-shaped curves normal curves? Explain.
- What is meant by a transformed score? Give an example.
- If a score is at the mean of a set of raw scores, where will it be if the set of raw scores is transformed to z scores? Why?
Chapter 10—Introduction to Hypothesis Testing Using the Sign Test
MULTIPLE CHOICE
- The nondirectional alternative hypothesis asserts that ____.
a. | the results of the experiment were due to chance alone |
b. | no conclusions can be drawn from the experiment |
c. | the independent variable has an effect |
d. | the independent variable has no effect |
- The statistic used in the sign test measures ____.
a. | the difference between the means of the two groups |
b. | the direction of the differences between pairs of scores |
c. | the magnitude of the differences between pairs of scores |
d. | the difference between the variance of the two groups |
- In the sign test, if the null hypothesis is true, then P ____.
a. | equals 0.50 |
b. | is greater than 0.50 |
c. | is less than 0.50 |
d. | differs depending on H_{1} |
- An alpha level of 0.05 indicates that ____.
a. | if H_{0} is true, the probability of falsely rejecting it is limited to 0.05 |
b. | 95% of the time, chance is operating |
c. | the probability of a Type II error is 0.05 |
d. | the probability of a correct decision is 0.05 |
- lf alpha is changed from 0.05 to 0.01, ____.
a. | the probability of a Type II error decreases |
b. | the probability of a Type I error increases |
c. | the error probabilities stay the same |
d. | the probability we will retain a false H_{0} increases |
- If you reject the null hypothesis, you may be making ____.
a. | a Type II error |
b. | a Type I error |
c. | a correct decision |
d. | a and c |
e. | b and c |
- If you retain the null hypothesis, you may be making ____.
a. | a Type II error |
b. | a Type I error |
c. | a correct decision |
d. | a and c |
e. | b and c |
- The sign test ____.
a. | analyzes the sign of difference scores |
b. | is used with a repeated measures design |
c. | uses the binomial distribution |
d. | evaluates the magnitude of the differences |
e. | all of the above |
f. | a, b and c |
- In the repeated measures design, ____.
a. | differences between paired scores are analyzed |
b. | the raw scores in each condition are analyzed separately |
c. | we must use a directional alternative hypothesis |
d. | all of the above |
- The null hypothesis which is appropriate for a directional alternative hypothesis asserts that ____.
a. | the independent variable has had no effect |
b. | chance alone is responsible for the differences between conditions |
c. | the independent variable does not have an effect in the direction predicted by H_{1} |
d. | b and c |
- If the alternative hypothesis states that alcohol affects short-term memory, the null hypothesis states ____.
a. | alcohol does not decrease short-term memory |
b. | alcohol has no effect on short-term memory |
c. | alcohol decreases short-term memory |
d. | P ¹ Q |
- If alpha equals 0.05 and the probability level of your experiment is 0.04, you would ____.
a. | reject the null hypothesis |
b. | retain the null hypothesis |
c. | accept the null hypothesis |
d. | redo the experiment |
- Using the sign test, if the null hypothesis is false, then P (the probability of a plus) ____.
a. | equals 0.50 |
b. | equals alpha |
c. | equals beta |
d. | is not equal to 0.50 |
- In an experiment with a repeated measures design ____.
a. | the entire experiment is done twice |
b. | one group of subjects receives one treatment, the other group receives another treatment |
c. | the same subjects receive both treatments |
d. | none of the above |
- If alpha is 0.05 and obtained probability level is 0.01, you could be making a ____.
a. | Type II error or correct decision |
b. | Type II error or a Type I error |
c. | Type I error or a correct decision |
d. | all of the above |
- If we set alpha at 0.05 instead of 0.01 ____.
a. | we have a greater risk of a Type I error |
b. | we have a greater risk of a Type II error |
c. | we have a lesser risk of a Type II error |
d. | a and c |
- If the alpha level is changed from 0.05 to 0.01, what effect does this have on beta?
a. | beta decreases |
b. | beta increases |
c. | beta is unaffected |
d. | cannot be determined |
- In stating H_{0} and H_{1}, one must be certain that they are ____.
a. | mutually exclusive |
b. | independent |
c. | exhaustive |
d. | a series of N trials |
e. | a and c |
- In an experiment involving a nondirectional alternative hypothesis, the obtained result was 7 pluses and 1 minus. To evaluate the null hypothesis, which of the following probabilities would you use?
a. | p(7) |
b. | p(7) + p(8) |
c. | p(0) + p(1) + p(7) + p(8) |
d. | p(1) + p(7) |
- When the results of an experiment are nonsignificant, the proper conclusion(s) is (are) ____.
a. | the experiment fails to show a real effect for the independent variable |
b. | chance alone is at work |
c. | accept H_{0} |
d. | accept H_{1} |
e. | the independent variable has no effect |
f. | a, b, c and e |
- It is important to know the possible errors (Type I or Type II) we might make when rejecting or retaining H_{0} ____.
a. | to minimize these errors when designing the experiment |
b. | to be aware of the fallacy of “accepting H_{0}“ |
c. | to maximize the probability of making a correct decision by proper design |
d. | all of the above |
e. | a and c |
- If a = 0.05_{1 tail} and the obtained result has a probability of 0.01 and is in the opposite direction to that predicted by H_{1}, we conclude by ____.
a. | rejecting H_{0} |
b. | retaining H_{0} |
c. | accepting H_{1} |
d. | accepting H_{0} |
- The alpha level ____.
a. | is always set at 0.05 or 0.01 |
b. | is set after the data are analyzed |
c. | is determined by the consequences of making a Type I and Type II error |
d. | depends on N |
- When the results are statistically significant, this means ____.
a. | the obtained probability is equal to or less than alpha |
b. | the independent variable has had a large effect |
c. | we can reject H_{0} |
d. | all of the above |
e. | a and c |
Exhibit 10-1
A psychologist is interested in whether hypnosis affects brain dominance. Twelve college students from the freshmen class are randomly sampled for an experiment. The experiment has two conditions which are given on different days. In condition 1, the students are hypnotized and then given a test which measures the relative dominance of the right and left hemispheres. The higher the score, the more dominant is the right hemisphere. In condition 2, the same students are given the test again, only this time they are not hypnotized but are in their normal state of consciousness. The following scores are obtained.
Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Condition 1 | 20 | 16 | 22 | 18 | 23 | 30 | 16 | 19 | 14 | 16 | 17 | 25 |
Condition 2 | 14 | 13 | 17 | 19 | 21 | 22 | 14 | 22 | 12 | 14 | 15 | 22 |
- Refer to Exhibit 10-1. The nondirectional alternative hypothesis is ____.
a. | hypnosis affects brain dominance |
b. | hypnosis does not affect brain dominance |
c. | hypnosis increases right brain dominance |
d. | hypnosis does not increase right brain dominance |
- Refer to Exhibit 10-1. The null hypothesis appropriate for the nondirectional alternative hypothesis is ____.
a. | hypnosis does not increase right brain dominance |
b. | hypnosis does not affect brain dominance |
c. | hypnosis does not increase left brain dominance |
d. | hypnosis affects brain dominance |
- Refer to Exhibit 10-1. The obtained probability = ____.
a. | 0.0161 |
b. | 0.0384 |
c. | 0.0192 |
d. | 0.0322 |
- Refer to Exhibit 10-1. Using a = 0.05_{2 tail}, your conclusion is ____.
a. | accept H_{0}; hypnosis has no affect on brain dominance |
b. | retain H_{0}; we cannot conclude that hypnosis affects brain dominance |
c. | reject H_{0}; hypnosis affects brain dominance |
d. | change H_{0} |
- Refer to Exhibit 10-1. The population to which these results apply is ____.
a. | all students |
b. | the 12 students in the experiment |
c. | the freshman class |
d. | all adults |
- Refer to Exhibit 10-1. If you reject H_{0}, the error(s) you may be making is (are) ____.
a. | a Type I error |
b. | a Type II error |
c. | that hypnosis may not affect brain dominance |
d. | a and c |
e. | b and c |
- Using the sign test, if (1) H_{1} is directional, (2) H_{0} is false, (3) a = 0.01, and (4) N = 12, then the probability of making a Type I error equals ____.
a. | 0.0002 |
b. | 0.0010 |
c. | 0 |
d. | 0.0192 |
- Using the sign test, with N = 15 and a = 0.05_{2-tail}, if H_{0} is true, the probability of making a Type I error equals ____.
a. | 0.0042 |
b. | 0 |
c. | 0.05 |
d. | 0.0352 |
e. | none of the above |
- If the result of an experiment is statistically significant, this means
a. | the result is reliable |
b. | the result is important |
c. | if we repeat the experiment, we expect the result to be significant again |
d. | a and c |
e. | a, b and c |
- If p (obtained) from an experiment equals 0.05 and alpha equals 0.05 (both two-tailed), what would you conclude?
a. | reject H_{0} |
b. | retain H_{0} |
c. | reject H_{1} |
d. | retain H_{1} |
- If you reject the null hypothesis, what type of error might you be making?
a. | Type I |
b. | Type II |
c. | Type III |
d. | cannot be determined |
- If alpha equals 0.05, how many times out of 100 would you expect to reject the null hypothesis when the null hypothesis is in fact true?
a. | 1 |
b. | 0.05 |
c. | 0.01 |
d. | 5 |
- lf we drew a random sample from an introductory psychology class, to whom could we generalize our results?
a. | all of human kind |
b. | the university |
c. | all psychology students |
d. | the students in that introductory psychology class |
- If we set alpha at 0.05 instead of 0.01, other factors held constant ____.
a. | we have a greater risk of a Type I error |
b. | we have a greater risk of a Type II error |
c. | we have a lower risk of a Type II error |
d. | a and c |
- If you reject H_{0} when H_{0} is false, you have made a ____.
a. | Type I error |
b. | Type II error |
c. | correct decision |
d. | none of the above |
- If the alpha level is changed from 0.05 to 0.01, what effect does this have on beta?
a. | beta decreases |
b. | beta increases |
c. | beta is unaffected |
d. | cannot be determined |
- The sign test can be used for ____.
a. | a repeated measures design |
b. | a replicated measures design |
c. | a correlated measures design |
d. | all of the above |
- One can say it is always preferable to make a Type II error.
a. | True |
b. | False |
c. | It depends on the costs of making a Type I or Type II error |
- In a nondirectional alternative hypothesis, evaluating the probability of observing 7 pluses out of 8 events equals ____.
a. | p(7) |
b. | p(7) + p(8) |
c. | p(0) + p(1) + p(7) + p(8) |
d. | p(0) + p(8) |
Exhibit 10-2
Refer to the following hypothetical data collected using replicated measures design:
Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
Pre | 50 | 49 | 37 | 16 | 80 | 42 | 40 | 58 | 31 | 21 |
Post | 56 | 50 | 30 | 25 | 90 | 44 | 60 | 71 | 32 | 22 |
- Refer to Exhibit 10-2. In a two-tailed test of H_{0} using a = 0.05, what is p(obtained) for the results shown?
a. | 0.0500 |
b. | 0.0108 |
c. | 0.1094 |
d. | 0.0216 |
- Refer to Exhibit 10-2. Find p(obtained) for a two-tailed test of H_{0} using a = 0.05. What would your conclusion be?
a. | reject H_{0} |
b. | accept H_{0} |
c. | retain H_{0} |
d. | retain H_{1} |
e. | b or c |
- Refer to Exhibit 10-2. What would you conclude using a = 0.01_{2 tail}?
a. | reject H_{0} |
b. | accept H_{0} |
c. | retain H_{0} |
d. | fail to reject H_{1} |
e. | b or c |
- Refer to Exhibit 10-2. What type error might you be making using a = 0.05_{2 tail}?
a. | Type I |
b. | Type II |
c. | Type III |
d. | cannot be determined |
- If the results of an experiment are statistically significant,
a. | the results must important |
b. | the results should be ignored |
c. | the results might important |
d. | the results are reliable |
e. | a and d |
f. | c and d |
- For any given obtained result, a one tail p-level is
a. | appropriate to use no matter what the alternative hypothesis states. |
b. | less than the two tail p-level |
c. | is appropriate to use only if the alternative hypothesis is directional |
d. | is appropriate to use only if the null hypothesis is nondirectional |
e. | b and c |
- If the results of an experiment allow rejection of the null hypothesis,
a. | the effect of the independent variable must be large. |
b. | similar results are likely to occur if the experiment is repeated |
c. | the experiment proves that H_{0} is false. |
d. | a and c |
e. | b and c |
TRUE/FALSE
- Regardless of whether H_{1} is directional or nondirectional, when evaluating H_{0} we always assume chance is responsible for the differences in results between conditions.
- Using the sign test, and excluding ties, if H_{0} is true the sample data must have half pluses and half minuses.
- If H_{0} is true and we reject it, we have made a Type I error.
- If H_{0} is false and we reject it, we have made a Type II error.
- If H_{0} is false, and we retain it, we have made a Type II error.
- We always evaluate just the specific result obtained in the experiment.
- We always evaluate the tail of the distribution, beginning with the obtained result, rather than just the obtained result itself.
- The alternative hypothesis must be nondirectional.
- We always directly evaluate H_{1} when analyzing the data.
- The sign test analyzes both the magnitude and direction of the data.
- The value used for alpha depends on the consequences of making a Type I and Type II error.
- It is always appropriate to use a directional alternative hypothesis.
- H_{1} and H_{0}, taken together, cover the entire continuum with regard to possible effects of the independent variable.
- If results are statistically significant, the independent variable must have had a large effect.
- It is technically correct to conclude by “accepting” rather than “failing to reject” H_{0}.
- If the result turns out to be in the direction opposite to a directional H_{1}, we must conclude by retaining H_{0}.
- It is permissible to use a directional H_{1 }when there are good theoretical as well as strong supporting data to justify the predicted direction.
- It is always appropriate to use a directional H_{1}.
- It is impossible to prove with certainty the truth of H_{1} when using sample data.
- If H_{0} is validly rejected, H_{1} must be true.
- The sign test is used with the replicated measures design.
- If alpha is made more stringent, beta increases.
- If H_{0} is true, beta equals 0.00.
DEFINITIONS
- Define alpha level.
.
- Define alternative hypothesis.
- Define beta.
- Define correlated groups design.
- Define directional hypothesis.
- Define fail to reject null hypothesis.
- Define important size of effect.
- Define nondirectional hypothesis.
- Define null hypothesis.
- Define one-tailed probability.
- Define reject null hypothesis.
- Define repeated measures design.
- Define replicated measures design.
- Define retain null hypothesis.
- Define significant.
- Define size of effect.
- Define state of reality.
- Define two-tailed probability.
- Define Type I error.
- Define Type II error.
SHORT ANSWER
- A psychologist is interested in whether hypnosis affects brain dominance. Twelve college students from the freshmen class are randomly sampled for an experiment. The experiment has two conditions which are given on different days. In condition 1, the students are hypnotized and then given a test which measures the relative dominance of the right and left hemispheres. The higher the score, the more dominant is the right hemisphere. In condition 2, the same students are given the test again, only this time they are not hypnotized but are in their normal state of consciousness. The following scores are obtained.
Student | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
Condition 1 | 20 | 16 | 22 | 18 | 23 | 30 | 16 | 19 | 14 | 16 | 17 | 25 |
Condition 2 | 14 | 13 | 17 | 19 | 21 | 22 | 14 | 22 | 12 | 14 | 15 | 22 |
a. | What is the alternative hypothesis? |
b. | What is the null hypothesis? |
c. | What do you conclude, using a = 0.05_{2 tail}? |
d. | What type error may you be making because of your conclusion in part c? |
e. | To what population do your results apply? (Please show all your work.) |
- Briefly describe the process involved in hypothesis testing, beginning with H_{1} and H_{0}, and ending with generalization to the population
- Define Type I and Type II error. Why is it important to know the possible errors we might make when rejecting or retaining H_{0}?
- When is it appropriate to use a directional hypothesis? Discuss.
- Why is alpha usually set at 0.05 or 0.01?
- Why do we directly evaluate H_{0} rather than H_{1}? Explain.
- If the obtained probability in an experiment equals 0.1500, then the probability that chance alone is at work equals 0.1500. Is this statement true? Explain.
- The null hypothesis for a directional H_{1} asserts that chance alone is at work or there is a real effect in the direction opposite to that predicted by H_{1}. This is a correct statement, and yet we reject or retain this H_{0} based on assuming chance alone is at work. What about the possibility of a real effect in the opposite direction?
- What do we mean by “state of reality”?
- Using the sign test, is the probability of making a Type I error equal to alpha? Why or why not? Illustrate, using an example and appropriate calculations.
- If a result is statistically significant, this means that the result must be an important one. Is this statement true? Explain
Chapter 17—Chi-Square and Other Nonparametric Tests
MULTIPLE CHOICE
- Chi-square is used to test differences between ____.
a. | proportions |
b. | means |
c. | variances |
d. | none of the above |
- The larger the discrepancy between f_{o} and f_{e} for each cell, ____.
a. | the more likely the results will not be significant |
b. | the more likely H_{0} will be rejected |
c. | the more likely the population proportions are the same |
d. | the more likely the population proportions are different |
e. | a and c |
f. | b and d |
- For any given alpha level, c^{2}_{crit} ____.
a. | increases with increases in N |
b. | decreases with increases in N |
c. | increases with increases in degrees of freedom |
d. | a and c |
- Chi-square should not be used if ____.
a. | df = 1 |
b. | f_{e} is below 5 |
c. | f_{o} is below 5 |
d. | f_{e} = f_{o} |
- Chi-square may be used with ____
a. | nominal data |
b. | ordinal data |
c. | interval data |
d. | ratio data |
e. | all of the above |
- To compute c^{2}, the entries in the contingency table should be ____.
a. | frequencies |
b. | means |
c. | variances |
d. | degrees of freedom |
- The degrees of freedom for a contingency table equal ____.
a. | rc – 1 |
b. | (r – 1)(c – 1) |
c. | (r – 1)(c) |
d. | (c – 1)(r) |
e. | N – 1 |
- In most situations, parametric tests ____.
a. | have the same power as nonparametric tests |
b. | are less powerful than nonparametric tests |
c. | are more powerful than nonparametric tests |
d. | are less sensitive than nonparametric tests |
e. | b and d |
- Which of the following are examples of parametric tests?
a. | t test |
b. | sign test |
c. | Mann-Whitney U test |
d. | Chi-square test |
e. | F test |
f. | a and e |
- Which of the following are examples of nonparametric tests?
a. | t test |
b. | sign test |
c. | Mann-Whitney U test |
d. | Chi-square test |
e. | F test |
f. | b, c and d |
g. | all of the above |
- Which of the following are true?
a. | f_{o} is the symbol for the observed frequency |
b. | f_{e} is the symbol for the expected frequency |
c. | c^{2} is the symbol for chi-square |
d. | all of the above |
- The sampling distribution of chi-square ____.
a. | is skewed |
b. | varies with df |
c. | is a theoretical distribution |
d. | all of the above |
e. | a and b |
- The c^{2} test is ____.
a. | always directional |
b. | never directional |
c. | generally nondirectional |
d. | generally directional |
- When evaluating c^{2}_{obt}, the critical region for rejection of H_{0} ____.
a. | lies under both tails of the distribution |
b. | lies under the right hand tail of the distribution |
c. | lies under the left hand tail of the distribution |
d. | lies in the middle of the distribution |
- A contingency table ____.
a. | is a two-way table |
b. | involves two variables |
c. | involves two mutually exclusive variables |
d. | all of the above |
e. | a and b |
- The computation of f_{e} ____.
a. | is based on population proportion estimates |
b. | is based on known population proportions |
c. | is based on population means |
d. | none of the above |
- In a 2 ´ 2 contingency table, if we keep the marginals at their observed values, how many f_{o} scores are free to vary?
a. | 3 |
b. | 0 |
c. | 1 |
d. | all of them |
- The Wilcoxon signed ranks test ____.
a. | is used with a correlated groups design |
b. | is used with data that is nominal in scaling |
c. | uses both the magnitude and direction of the data |
d. | all of the above |
e. | a and b |
- If N = 18 and a = 0.05_{2 tailed}, the value of T_{crit} is ____.
a. | 40 |
b. | ±40 |
c. | -40 |
d. | 47 |
- If a = 0.05, and df = 4, the value of c^{2}_{crit} = ____.
a. | 9.488 |
b. | 0.711 |
c. | 7.815 |
d. | 11.070 |
Exhibit 17-1
Prior to a recent gubernatorial election, a survey was conducted to determine whether there was a relationship between sexual gender and preference for the Democratic or Republican candidate. The following data were recorded.
- Refer to Exhibit 17-1. The value of c^{2}_{obt} = ____.
a. | 2.06 |
b. | 2.09 |
c. | 1.80 |
d. | 1.75 |
- Refer to Exhibit 17-1. The value of df = ____.
a. | 2 |
b. | 1 |
c. | 3 |
d. | need more information |
- Refer to Exhibit 17-1. Using a = 0.05, c^{2}_{crit} = ____.
a. | 3.841 |
b. | 5.412 |
c. | 2.706 |
d. | -3.841 |
- Refer to Exhibit 17-1. Using a = 0.05, what is your conclusion?
a. | accept H_{0}; there is no relationship between sex and candidate preference |
b. | reject H_{0}; there is a significant relationship between sex and candidate preference |
c. | retain H_{0}; the study does not show a significant relationship between sex and candidate preference |
d. | retain H_{0}; this study shows a significant relationship between sex and candidate preference |
Exhibit 17-2
A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression.
Individuals | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Sunshine | 10 | 12 | 14 | 11 | 12 | 10 | 14 | 15 |
No sunshine | 20 | 21 | 17 | 14 | 18 | 8 | 18 | 14 |
- Refer to Exhibit 17-2. Using the Wilcoxon signed ranks test, the value of T_{obt} is ____.
a. | -3 |
b. | 3 |
c. | 33 |
d. | 4 |
- Refer to Exhibit 17-2. Using a = 0.05_{2 tail}, T_{crit} = ____.
a. | 2 |
b. | 5 |
c. | ±3 |
d. | 3 |
- Refer to Exhibit 17-2. Using a = 0.05_{2 tail}, what do you conclude? Assume for the purpose of this question that sunshine was the only systematic difference between the conditions.
a. | reject H_{0}; sunshine appears to affect depression |
b. | reject H_{0}; sunshine has no effect on depression |
c. | retain H_{0}; we cannot conclude that sunshine affects depression |
d. | accept H_{0}; sunshine affects depression |
- Which of the following are nonparametric tests?
a. | sign test |
b. | Wilcoxon test |
c. | Mann-Whitney U test |
d. | Kruskal-Wallis test |
e. | all of the above |
f. | a, b and c |
- The Mann-Whitney U test can be used with ____.
a. | nominal data |
b. | interval data |
c. | ordinal data |
d. | ratio data |
e. | all of the above |
f. | b, c and d |
- Generally, if R_{1} is greater than R_{2}, ____.
a. | the equation yields the U value |
b. | the equation yields the U value |
c. | the power of the test is necessarily low |
d. | we must reject H_{0} |
- As the separation between the two groups of scores increases, U_{obt} ____.
a. | increases |
b. | decreases |
c. | stays the same |
d. | approaches U ^{‘}_{obt} |
- In the Mann-Whitney U test, the U value of 0 ____.
a. | represents a low degree of separation between the two groups |
b. | implies that the two groups are identical |
c. | represents the greatest degree of separation between the two groups |
d. | indicates that the power of the experiment is very low. |
- The statistics (U or U’) used in the Mann-Whitney U test, measure ____.
a. | the differences between the means of the two groups |
b. | the direction of the differences between pairs of scores |
c. | the power of the experiment |
d. | the separation between the two groups |
- A Mann-Whitney U value of zero indicates ____.
a. | you can reject the null hypothesis |
b. | low degree of separation between the scores of each group |
c. | zero difference between the two groups |
d. | high degree of separation between the scores of each group |
- U + U’ equals ____.
a. | n |
b. | n_{1} + n_{2} |
c. | n_{1} ´ n_{2} |
d. | none of the above |
- The Mann-Whitney U test is used with ____.
a. | an independent groups design |
b. | a replicated measures design |
c. | a correlated groups design |
d. | b and c |
- The Mann-Whitney U test uses ____.
a. | only the direction of the scores |
b. | only the magnitude of the scores |
c. | both the magnitude and direction of the scores |
d. | none of the above |
Exhibit 17-3
Consider the following set of scores:
25, 28, 28, 28, 30
- Refer to Exhibit 17-3. In assigning ranks to the scores, a score of 28 receives a rank of ____.
a. | 2.5 |
b. | 2 |
c. | 4 |
d. | 3 |
- Refer to Exhibit 17-3. A score of 30 would receive a rank of ____.
a. | 4 |
b. | 5 |
c. | 3 |
d. | 0 |
- If n_{1} = 5, n_{2} = 4, and a = 0.01_{2 tail}, the power of the Mann-Whitney U test equals ____.
a. | 1 |
b. | 0 |
c. | 0.01 |
d. | need more information |
- If n_{1} = 6, n_{2} = 8 and a = 0.05_{2 tail}, U_{crit} value is ____.
a. | 8 |
b. | 40 |
c. | 6 |
d. | 42 |
Exhibit 17-4
A student at a Midwest college is interested in whether Psychology majors spend more or less time studying than English majors. She randomly selects 8 Psychology majors and 8 English majors and determines their weekly studying time. The following are the scores. Note one person dropped out of the study.
Psychology Majors | 16 | 12 | 13 | 10 | 9 | 10 | 8 | |
English Majors | 10 | 25 | 15 | 17 | 23 | 14 | 19 | 18 |
- Refer to Exhibit 17-4. The value of U_{obt} is ____.
a. | 6 |
b. | 50 |
c. | 14 |
d. | 42 |
- Refer to Exhibit 17-4. If a = 0.05_{2 tail,} U_{crit} = ____.
a. | 7 |
b. | 10 |
c. | 46 |
d. | 49 |
- Refer to Exhibit 17-4. Using a = 0.05_{2 tail}, what do you conclude?
a. | reject H_{0}; there is a significant difference in the amount of time Psychology and English majors study |
b. | reject H_{0}; there is no difference in the amount of time Psychology and English majors study |
c. | accept H_{0}; there is no difference in the amount of time Psychology and English majors study |
d. | retain H_{0}; there is no difference in the amount of time Psychology and English majors study |
- The statistic used with the Kruskal-Wallis test is ____.
a. | F_{obt} |
b. | H_{obt} |
c. | U_{obt} |
d. | t_{obt} |
Exhibit 17-5
A researcher conducts a one-way ANOVA involving three groups. When she analyzes the data she realizes the data seriously violate the assumptions underlying parametric ANOVA. Therefore, she decides to use the Kruskal-Wallis test to conclude with regard to H_{0}. The data are given below.
(1) | (2) | (3) |
6
10 12 16 14 7 |
8
12 9 15 17 11 |
12
13 20 18 22 15 |
- Refer to Exhibit 17-5. H_{obt} = ____.
a. | 4.25 |
b. | 5.43 |
c. | 2.68 |
d. | 6.86 |
- Refer to Exhibit 17-5. Using a = 0.05, H_{crit} = ____.
a. | 9.210 |
b. | 7.815 |
c. | 5.991 |
d. | 7.824 |
- Refer to Exhibit 17-5. What is the appropriate conclusion concerning H_{0}?
a. | reject H_{0}; the independent variable has a real effect |
b. | accept H_{0}; the independent variable has no effect |
c. | retain H_{0}; the independent variable has a real effect |
d. | retain H_{0}; we cannot conclude the independent variable has a real effect |
- The c^{2} test can be used for variables with ____ scaling as long as the categories are mutually exclusive.
a. | nominal |
b. | ordinal |
c. | interval |
d. | ratio |
e. | all of the above |
- The ____ test is the most powerful test for a repeated measures design.
a. | sign |
b. | t |
c. | Wilcoxin signed ranks |
d. | all of the tests are equally powerful |
- Which of the following tests are parametric statistical tests:
a. | sign test |
b. | chi-square test |
c. | Wilcoxin signed ranks test |
d. | none of the above |
- If an experiment using frequency data tested the preference for 6 brands of soup, there would be ____ degrees of freedom.
a. | 1 |
b. | N – 1 |
c. | 5 |
d. | 6 |
Exhibit 17-6
The following question(s) pertain to the table below.
- Refer to Exhibit 17-6. The value of c^{2}_{obt }for the table above is ____. (Assume equal probabilities for f_{e} in each cell.)
a. | 96.00 |
b. | 9.42 |
c. | 8.13 |
d. | 13.28 |
- Refer to Exhibit 17-6. The value of c^{2}_{crit} for the table above with a = 0.01 is ____.
a. | 6.635 |
b. | 15.086 |
c. | 13.277 |
d. | 11.668 |
- Refer to Exhibit 17-6. Based on the table above, calculate the value of c^{2}_{crit} with a = 0.01. Your conclusion is to ____.
a. | reject H_{0} |
b. | reject H_{1} |
c. | retain H_{0} |
d. | retain H_{1} |
Exhibit 17-7
The following question(s) pertain to the table below.
- Refer to Exhibit 17-7. The value of f_{e} for the cell in row W, column A is ____.
a. | 24.9 |
b. | 3.2 |
c. | 16.0 |
d. | 63.0 |
- Refer to Exhibit 17-7. The value of c^{2}_{obt} for the table above is ____.
a. | 19.01 |
b. | 21.38 |
c. | 24.87 |
d. | 16.82 |
- Refer to Exhibit 17-7. The value of c^{2}_{crit} for the table above with a = 0.05 is ____.
a. | 13.277 |
b. | 7.779 |
c. | 3.841 |
d. | 9.488 |
- Refer to Exhibit 17-7. Calculate the value of f_{e} for the cell in row W, column A. Your conclusion is ____.
a. | to reject H_{0} |
b. | to reject H_{1} |
c. | to retain H_{0} |
d. | fail to accept H_{1} |
Exhibit 17-8
The following question(s) pertain to the table below.
- Refer to Exhibit 17-8. For the table above there is(are) ____ degrees of freedom.
a. | k – 1 |
b. | 1 |
c. | 2 |
d. | 4 |
- Refer to Exhibit 17-8. The value of c^{2}_{obt} for the table above is ____.
a. | 47.43 |
b. | 17.96 |
c. | 4.07 |
d. | 9.71 |
- For a low value of df the c^{2} distribution is ____.
a. | normally distributed |
b. | positively skewed |
c. | negatively skewed |
d. | none of the above |
- The value of T_{obt} for the following data is ____.
a. | 21 |
b. | -6 |
c. | 15 |
d. | 6 |
- If there are 16 subjects in a repeated measures design then the sum of the unsigned ranks equals ____.
a. | 136 |
b. | 68 |
c. | 272 |
d. | 32 |
- If T_{obt} = 12 and T_{crit} = 10, one would ____.
a. | reject H_{0} |
b. | retain H_{0} |
c. | accept H_{0} |
d. | reject H_{1} |
- The statistics used for the Mann-Whitney U test measure ____.
a. | the mean differences between the two groups |
b. | the direction of the differences between pairs of scores |
c. | the power of the experiment |
d. | the separation between the two sets of scores |
- Consider the following set of scores: 81, 83, 84, 84, 87. What rank would you give to a score of 84?
a. | 3 |
b. | 3.5 |
c. | 4 |
d. | 4.5 |
Exhibit 17-9
The following question(s) pertain to the data below.
- Refer to Exhibit 17-9. The value of U_{obt} (not U’_{obt}) is ____.
a. | 14.5 |
b. | 20.5 |
c. | 21.5 |
d. | 27.5 |
- Refer to Exhibit 17-9. The value of U_{crit} using a = 0.05_{2 tail} is ____.
a. | 36 |
b. | 5 |
c. | 6 |
d. | 30 |
- Refer to Exhibit 17-9. The conclusion using a = 0.05_{2 tail} is ____.
a. | reject H_{0} |
b. | reject H_{1} |
c. | retain H_{0} |
d. | retain H_{1} |
Exhibit 17-10
In Chapter 16, we presented the data from an independent groups design and asked if it was appropriate to use parametric ANOVA. The data are presented again below. The correct answer was that it was not appropriate to use parametric ANOVA because of unequal n‘s and homogeneity of variance assumption violation.
- Refer to Exhibit 17-10. Is it possible to analyze the data with an alternate test?
a. | yes |
b. | no |
- Refer to Exhibit 17-10. If it is possible to analyze the data with an alternate test, what is the name of the test?
a. | t test for independent groups |
b. | F test |
c. | Kruskal-Wallis |
d. | Mann-Whitney U test |
- Refer to Exhibit 17-10. H_{obt} = ____.
a. | 10.25 |
b. | 10.63 |
c. | 15.96 |
d. | 5.96 |
- Refer to Exhibit 17-10. What are the df?
a. | 1 |
b. | 2 |
c. | 3 |
d. | need more information |
- Refer to Exhibit 17-10. Using a = 0.05, H_{crit} = ____.
a. | 3.841 |
b. | 7.815 |
c. | 5.991 |
d. | 7.824 |
- Refer to Exhibit 17-10. What do you conclude, using a = 0.05?
a. | retain H_{0}; There is no difference in the populations. |
b. | accept H_{0}; There is no difference in the populations. |
c. | reject H_{0}; At least one of the population means differs from at least one of the others. |
d. | reject H_{0}; At least one of the distributions differs from at least one of the others. |
TRUE/FALSE
- All inference tests depend on population characteristics.
- Parametric tests depend less on population characteristics than nonparametric tests.
- Parametric tests are more versatile than nonparametric tests.
- c^{2}_{obt} cannot be negative.
- To find f_{e} for any cell, multiply the marginals for that cell and divide by N.
- The Wilcoxin signed ranks test is less powerful than the sign test.
- To use the Wilcoxin signed ranks test, the difference scores must be at least of ordinal scaling.
- An assumption of c^{2} is that the scores in each cell are independent.
- The Wilcoxin signed ranks test is more powerful than the t test for correlated groups.
- Using c^{2}, the closer the observed frequency of each cell is to the expected frequency for that cell, the higher the probability of rejecting H_{0}.
- In order to reject the null hypothesis, c^{2}_{obt} ³ c^{2}_{crit}.
- The c^{2 } distribution is a family of curves that vary with degrees of freedom.
- The c^{2} test answers questions about population proportions.
- For valid use of chi-square, each subject can only have one entry in the table, and the table entries must be frequencies.
- Parametric tests are always more desirable than nonparametric tests.
- The Mann-Whitney U test makes no assumption about the shape of the population scores.
- The Mann-Whitney U test is used with a repeated measures design.
- If U_{obt} and U’_{obt} are equal, there is little overlap between the groups.
- U = 0 is the lowest possible U value.
- U = 0 indicates the greatest degree of separation between the groups.
- Generally, U’_{obt} < U_{obt}.
- The Mann-Whitney U test can only be used to analyze directional alternative hypotheses.
- The Mann-Whitney U test analyzes the separation between the groups.
- The data must be at least interval in scaling to use the Mann-Whitney U test.
- The Mann-Whitney U test uses both the magnitude and direction of the scores.
- U_{obt} and U’_{obt} yield the same information with regard to the degree of separation.
- The Kruskal-Wallis test is used as a substitute for parametric one-way ANOVA.
- The Kruskal-Wallis test assumes population normality.
- The Kruskal-Wallis test requires only ordinal scaling of the dependent variable.
- When using the Kruskal-Wallis test, tied scores between conditions are thrown out.
- The Kruskal-Wallis test requires there are at least 5 scores in each sample.
DEFINITIONS
- Define chi-square (c^{2}).
- Define contingency table.
- Define degree of separation.
- Define expected frequency (f_{e}).
- Define Kruskal-Wallis test.
- Define Mann-Whitney U test.
- Define marginals.
- Define observed frequency (f_{o}).
- Define Wilcoxon matched pairs signed ranks test.
SHORT ANSWER
- What distinguishes parametric from nonparametric tests? Give some examples.
- When might we use a nonparametric test? Give an example.
- What are the assumptions underlying the Kruskal-Wallis test?
- What are the assumptions underlying the chi-square test?
- What are the assumptions underlying the Mann-Whitney U test?
- What are the assumptions underlying the Wilcoxon signed ranks test?
- What is a contingency table?
- In analyzing the data from a two-way contingency table, involving variables A and B, what is the null hypothesis. Be specific using variables A and B, and the terms “proportions”, “frequency”, and “independent”.
- Identify the most sensitive, alternate nonparametric test for the following: t test for correlated groups, t test for independent groups, one-way, independent groups ANOVA.
- What variable does the Mann-Whitney U test measure to determine if the IV has had a real effect? What is the relationship between this variable and the real effect of the IV that makes this variable legitimate to use?
- The section, “What Is The Truth–Statistics and Applied Social Research–Useful or Abuseful’?” p. 480, raises some important issues. After reading that section, please answer the following questions.
a. | Do you think it ethical if social scientists with strong political views go out deliberately and do research biasing their questionnaires so that data will confirm their political views? How do you justify your answer? |
b. | If an organization conducts socially relevant research and the findings turn out to be against the interest of the organization, does the company have the moral obligation to inform the public? How do you justify for your answer? |
c. | Do drug companies have an ethical responsibility to report the outcomes of experiments they fund involving their drugs when the outcomes show their product to be inferior or no better than competing drugs? How do you justify your answer? |
- Is it true that parametric tests are generally more powerful than nonparametric tests? If so, give two reasons why we might choose to use a nonparametric test instead of a parametric test.
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