Deck 15: B:nonparametric Statistics

Question 1

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 either to the left or to the right of distribution 2, based on samples of sizes = 7 and = 9.
a. Should you use or as the test statistic?
b. What is the rejection region for the test if
c. What is the rejection region for the test if

Answer 1

a. If the test is two-tailed, you should use the smaller of That is, the test statistic is T = min ( ).
b. Since the test is two-tailed with = 0.05, half of this probability should be placed in each of the two tails. From the table of critical values for the Wilcoxon rank sum test (2.5% points), will be rejected if T = min 40.
c. From the table of critical values for the Wilcoxon rank sum test (0.5% points), will be rejected if T = min 35.

Question 2

Because of the rising costs of industrial accidents, many chemical, mining, and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses designed to heighten safety awareness. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1 and another eight take course 2. Each employee writes a test, which is marked out of a possible 25. The results are shown below. Do these data provide sufficient evidence at the 5% level of significance to conclude that the marks from course 2 are higher than those of course 1? Assume that the scores are not normally distributed.

Answer 2

The two population locations are the same. The location of population 1 (course 1) is to the left of the location of population 2 (course 2).
Rejection region: Test statistic: Conclusion: Don't reject the null hypothesis. The two population locations are the same.

Question 3

In testing the hypotheses, The two population locations are the same, and The location of population 1 is to the left of the location of population 2, the statistics , , , and are calculated with data drawn from two independent samples.
a. Which test is used for testing the hypotheses above?
b. What is the value of the test statistic?
c. What is the rejection region for this test at = 0.05?
d. What is your conclusion at = 0.05?

Answer 3

a. The Wilcoxon rank sum test
b. T = c. Reject if T 31
d. Don't reject the null hypothesis. The two population locations are the same.

Question 4

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Determine the rejection region for the Wilcoxon signed-rank test at the 5% significance level.

Question 5

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. State the null and alternative hypotheses.

Question 6

In an investigation of the visual scanning behaviour of hearing-impaired children, measurements of eye movement rates were taken on nine hearing-impaired children and nine hearing children as shown in the table below. Does it appear that the distributions of eye-movement rates for hearing-impaired children and hearing children differ? Test at = 0.05 using the Wilcoxon rank sum test.

Question 7

To investigate the effect of sleep on basal metabolism, seven students who averaged seven or more hours of sleep a night (Group A), and five students who averaged less than seven hours of sleep a night (Group B), were examined and their basal metabolism recorded as shown below. Since it was not clear whether the assumptions for a t test were valid, the researcher decided to employ nonparametric methods. Use the Wilcoxon rank sum test to determine whether the metabolism measurements for Group A are significantly higher than those of Group B. Use = 0.05.

Question 8

In testing the hypotheses, The two population locations are the same, and The two population locations are different, the statistics , , , and are calculated with data drawn from two independent samples.
a. Which test is used for testing the hypotheses above?
b. What is the value of the test statistic?
c. What is the rejection region for this test at = 0.05?
d. What is your conclusion at = 0.05?

Question 9

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. At what level of significance could we reject ?

Question 10

Suppose you want to use the Wilcoxon rank sum test to detect a shift in distribution 1 to the right of distribution 2, based on samples of sizes = 7 and = 9.
a. Should you use or as the test statistic?
b. What is the rejection region for the test if
c. What is the rejection region for the test if

Question 11

The following statistics are drawn from two independent samples: , ; , . Test at the 5% significance level to determine whether the two population locations differ.

Question 12

A vendor was interested in determining whether two soft drink machines dispense the same amount of liquid. A sample of size seven was selected from each machine and the amount of liquid dispensed (in mL) was recorded as follows: Use the Wilcoxon rank sum test to determine whether the distributions for the amount of liquid dispensed are the same for both machines. Use = 0.05.

Question 13

Given the statistics , , , , use the Wilcoxon rank sum test to determine at the 5% significance whether the location of population 1 is to the right of the location of population 2.

Question 14

Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ.
Sample 1: 17 20 18 25 16 22
Sample 2: 17 25 33 38 15 26 21

Question 15

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. State the null and alternative hypotheses if the Wilcoxon signed-rank test is used on the data to see if we can conclude that the motion picture was successful in changing attitudes.

Question 16

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Is this a one-tailed test or a two-tailed test? Find the rejection region for = 0.10.

Question 17

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.

-Refer to Attitude Test Narrative. Using $\alpha$ = 0.10, can we conclude the motion picture was successful in changing attitudes?

Question 18

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Describe what the test statistic is for the Wilcoxon signed-rank test. What is the value of the test statistic in this ?

Question 19

Use the Wilcoxon rank sum test on the data below to determine at the 10% significance level whether the two population locations differ.
Sample 1: 32 22 19 29 20 34 25 9 28 17
Sample 2: 29 20 18 27 19 23 19 12 22 10

Question 20

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Describe what the test statistic is for the sign test. What is the value of the test statistic in this ?

Question 21

Ice Cream Narrative
A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand as better, 4 say that the brands taste the same, and the rest claim that the supermarket brand is better.
Refer to Ice Cream Narrative. Which test is appropriate for this situation?

Question 22

A matched pairs experiment yielded the following results:
Number of positive differences = 20
Number of negative differences = 8
Number of 0 differences = 2
Can we infer at the 5% significance level that the location of population 1 is to the right of the location of population 2? Justify your response.

Question 23

Typing Speed Narrative
Ten secretaries were selected at random from among the secretaries of a large university. The typing speed (number of words per minute) was recorded for each secretary on two different brands of computer keyboards. Assume that the typing speeds are not normally distributed. The following results were obtained.
Refer to Typing Speed Narrative. Perform the test you suggested in the question above to determine if these data provide enough evidence at the 5% significance level to infer that the brands differ with respect to typing speed.

Question 24

TV Commercials Narrative
It is important to sponsors of television shows that viewers remember as much as possible about the commercials. The advertising executive of a large company is trying to decide which of two commercials to use on a weekly half-hour comedy. To help make a decision, she decides to have 12 individuals watch both commercials. After each viewing, each respondent is given a quiz consisting of 10 questions. The number of correct responses was recorded and is listed below. Assume that the quiz results are not normally distributed.
Quiz Scores
Refer to TV Commercials Narrative. Do these data provide enough evidence at the 5% significance level to conclude that the two commercials differ? Justify your conclusion.

Question 25

Books Manuscripts Narrative
In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better.
Refer to Books Manuscripts Narrative. Can Duxbury conclude at the 5% significance level that manuscript 2 is more highly rated than manuscript 1?

Question 26

Books Manuscripts Narrative
In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better.
Refer to Books Manuscripts Narrative. Explain how to use the p-value for testing the hypotheses at the 5% significance level.

Question 27

TV Commercials Narrative
It is important to sponsors of television shows that viewers remember as much as possible about the commercials. The advertising executive of a large company is trying to decide which of two commercials to use on a weekly half-hour comedy. To help make a decision, she decides to have 12 individuals watch both commercials. After each viewing, each respondent is given a quiz consisting of 10 questions. The number of correct responses was recorded and is listed below. Assume that the quiz results are not normally distributed.
Quiz Scores
Refer to TV Commercials Narrative. Which test is appropriate for this situation?

Question 28

A car dealer was interested in comparing two brands of tires to see if they yielded different wear length (in thousands of km). The dealer selected eight cars at random and used each of the brands of tires on each car. The wear length was recorded as follows: Use the sign test to see if the distribution of wear length is the same for both brands of tires. Use = 0.05.

Question 29

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Find the p-value for the Wilcoxon signed-rank test.

Question 30

Ice Cream Narrative
A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand as better, 4 say that the brands taste the same, and the rest claim that the supermarket brand is better.
Refer to Ice Cream Narrative. What is the p-value of the test in the previous question?

Question 31

Gourmet Meals Narrative
Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other?
Refer to Gourmet Meals Narrative. . Compare the results of the previous two questions.

Question 32

Ice Cream Narrative
A supermarket chain has its own house brand of ice cream. The general manager claims that her ice cream is better than the ice cream sold by a well-known ice cream parlour chain. To test the claim, 40 individuals are randomly selected to participate in the following experiment. Each respondent is given the two brands of ice cream to taste (without any identification) and asked to judge which one is better. Suppose that 25 people judge the ice cream parlour brand as better, 4 say that the brands taste the same, and the rest claim that the supermarket brand is better.
Refer to Ice Cream Narrative. Can we conclude at the 1% significance level that the general managers' claim is false? Justify your answer.

Question 33

Books Manuscripts Narrative
In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better.
Refer to Books Manuscripts Narrative. What is the p-value of the test you conducted in the previous question?

Question 34

Attitude Test Narrative
Twenty students are given an attitude test before and after viewing a motion picture designed to change their attitudes favourably toward a new curriculum. A high score indicates a favourable attitude and a low score indicates an unfavourable attitude, with the scores ranging from 1 to 30. This will use the sign test on the data given below to see if we can conclude the motion picture was successful in improving attitudes.
Refer to Attitude Test Narrative. Using the answers to the previous two questions, can we conclude that the motion picture was successful in changing attitudes?

Question 35

Gourmet Meals Narrative
Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other?
Refer to Gourmet Meals Narrative. Test by using the sign test with a value of near 0.05. Use the binomial tables to find the exact rejection region for the test.

Question 36

A paired-difference experiment was conducted to compare two populations. The data are shown in the table. Use a sign test to determine whether the population distributions are different.
Pairs
a. State the null and alternative hypotheses for the test.
b. Determine an appropriate rejection region with 0.01.
c. Calculate the observed value of the test statistic.
d. Do the data present sufficient evidence to indicate that populations 1 and 2 are different?

Question 37

Gourmet Meals Narrative
Two gourmets, A and B, rated 22 meals on a scale of 1 to 10. The data are shown in the table. Do the data provide sufficient evidence to indicate that one of the gourmets tends to give higher ratings than the other?
Refer to Gourmet Meals Narrative. Use the large-sample z statistic for testing. (Note: Although the large-sample approximation is suggested for 25, it works fairly well for values of n as small as 15).

Question 38

Typing Speed Narrative
Ten secretaries were selected at random from among the secretaries of a large university. The typing speed (number of words per minute) was recorded for each secretary on two different brands of computer keyboards. Assume that the typing speeds are not normally distributed. The following results were obtained.
Refer to Typing Speed Narrative. Which test is appropriate for this situation?

Question 39

A dog kennel manager was interested in determining whether there is a difference in the time it takes a dog to complete an obstacle course for two different courses. A random sample of 36 dogs was selected and the time it took each dog to complete each course was recorded. In 12 cases it took the dog longer to complete course 1. Use the normal approximation to the sign test to determine if there is a significant difference in the time it takes to complete the two obstacle courses. Use = 0.05.

Question 40

Books Manuscripts Narrative
In general, before an academic publisher agrees to publish a book, each manuscript is thoroughly reviewed by university professors. Suppose that the Duxbury Publishing Company has recently received two manuscripts for statistics books. To help them decide which one to publish, both are sent to 30 professors of statistics who rate the manuscripts to judge which one is better. Suppose that 10 professors rate manuscript 1 better and 20 rate manuscript 2 better.
Refer to Books Manuscripts Narrative. Which test is appropriate for this situation?

Question 41

Advertisement Narrative
In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and .
Refer to Advertisement Narrative. Conduct the test at the 5% significance level.

Question 42

In testing the hypotheses, The two population locations are the same vs. The two population locations are different, the statistics , , and are calculated with data drawn from a matched pairs experiment.
a. Which test is used for testing the hypotheses above?
b. What is the value of the test statistic?
c. What is the p-value of this test?
d. Can we infer at the 5% significance level that the population locations differ?

Question 43

Customers' Ages Narrative
The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed.
Customers' Ages
Refer to Customers' Ages Narrative. Do these data provide enough evidence at the 10% significance level to infer that there are differences in ages among the customers of the three restaurants? Justify your response.

Question 44

Three treatments were compared using a completely randomized design. The data are shown in the table. Do the data provide sufficient evidence to indicate a difference in location for at least two of the population distributions? Test using the Kruskal-Wallis H statistic with = 0.05.

Question 45

Advertisement Narrative
In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and .
Refer to Advertisement Narrative. What is the most accurate statement that can be made about the p-value of this test?

Question 46

Movie Ratings Narrative
A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of the most recently watched movies. The rating categories were 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each respondent was also asked to categorize his or her age as either 1 = teenager, 2 = young adult (20-34), 3 = middle age (35-50), and 4 = senior (over 50).
The results are shown below.
Refer to Movie Ratings Narrative. What statement can be made about the p-value for this test?

Question 47

A computer laboratory manager was interested in whether there was a difference in functioning time before needing to be recharged for three battery packs for laptop computers. The manager took a random sample of six battery packs of each brand and tested them. The results, in hours of functioning before needing to be recharged, were recorded as follows: The manager, unsure that the assumptions for the usual parametric analysis of variance were valid, decided to employ nonparametric methods. Use the appropriate nonparametric procedure to determine whether the distribution of functioning time before needing to be recharged is the same for the three brands of battery packs. Use = 0.05.

Question 48

Customers' Ages Narrative
The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed.
Customers' Ages
Refer to Customers' Ages Narrative. Using the appropriate statistical table, what statement can be made about the p-value for this test?

Question 49

Suppose you wish to detect a difference in the locations of two population distributions based on a paired-difference experiment consisting of n = 35 pairs.
a. Give the null and alternative hypotheses for the Wilcoxon signed-rank test.
b. Give the test statistic.
c. Give the rejection region for the test for = 0.05.
d. If = 339, what are your conclusions? [Note: = n(n + 1)/2].
e. Conduct the test using the large-sample z test. Compare your results with the nonparametric test results in the previous question.

Question 50

Advertisement Narrative
In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and .
Apply the Kruskal-Wallis test to determine if there is enough evidence at the 5% significance level to infer that at least two populations differ.
Sample

Question 51

Two aptitude tests are currently being used to screen applicants for a certain position within a company. The question arose as to whether the two tests are comparable, i.e., whether they yield the same results. Six applicants were selected at random to take both tests (in a random order). The following scores were recorded: Use the Wilcoxon signed-rank test to determine whether there is a difference in scores between the two tests. Use = 0.10.

Question 52

Given the statistics , , and n = 50 from a matched pairs experiment, perform the Wilcoxon signed-rank test to determine whether we can infer at the 5% significance level that the two population locations differ.

Question 53

Customers' Ages Narrative
The marketing manager of a pizza chain is in the process of examining some of the demographic characteristics of her customers. In particular, she would like to investigate the belief that the ages of the customers of pizza parlours, hamburger emporiums, and fast-food chicken restaurants are different. As an experiment, the ages of eight customers of each of the restaurants are recorded and listed below. From previous analysis we know that the ages are not normally distributed.
Customers' Ages
Refer to Customers' Ages Narrative. Explain how to use the p-value for testing the hypotheses.

Question 54

Heart Rates and Exercise Narrative
An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten men were randomly selected from each of four age groups: 10-19, 20-39, 40-59, and 60-69. Each man walked a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate (the difference before and after exercise) was recorded (in beats per minute). The data are shown in the table.
Refer to Heart Rates and Exercise Narrative. Do the data present sufficient evidence to indicate differences in location for at least two of the four age groups? Test using the Kruskal-Wallis H test with = 0.01.

Question 55

Movie Ratings Narrative
A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of the most recently watched movies. The rating categories were 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each respondent was also asked to categorize his or her age as either 1 = teenager, 2 = young adult (20-34), 3 = middle age (35-50), and 4 = senior (over 50).
The results are shown below.
Refer to Movie Ratings Narrative. Do these data provide sufficient evidence to infer at the 5% significance level that there were differences in ratings among the different age categories? Justify your response.

Question 56

Eight people were asked to perform a simple puzzle-assembly task under normal conditions and under stressful conditions. During the stressful time, a mild shock was delivered to subjects 3 minutes after the start of the experiment and every 30 seconds thereafter until the task was completed. Blood pressure readings were taken under both conditions. The data in the table are the highest readings during the experiment. Do the data present sufficient evidence to indicate higher blood pressure readings under stressful conditions? Analyze the data using the Wilcoxon signed-rank test for a paired experiment.

Question 57

Movie Ratings Narrative
A movie critic wanted to determine whether or not moviegoers of different age groups evaluated a movie differently. With this objective, he commissioned a survey that asked people their ratings of the most recently watched movies. The rating categories were 1 = terrible, 2 = fair, 3 = good, and 4 = excellent. Each respondent was also asked to categorize his or her age as either 1 = teenager, 2 = young adult (20-34), 3 = middle age (35-50), and 4 = senior (over 50).
The results are shown below.
Refer to Movie Ratings Narrative. Which test can the movie critic use in this situation?

Question 58

Advertisement Narrative
In a Kruskal-Wallis test to determine whether differences exist among three different advertisements, the following statistics were obtained: , , , , and .
Refer to Advertisement Narrative. Explain how to use the p-value for testing the hypotheses.

Question 59

Heart Rates and Exercise Narrative
An experiment was conducted to examine the effect of age on heart rate when a person is subjected to a specific amount of exercise. Ten men were randomly selected from each of four age groups: 10-19, 20-39, 40-59, and 60-69. Each man walked a treadmill at a fixed grade for a period of 12 minutes, and the increase in heart rate (the difference before and after exercise) was recorded (in beats per minute). The data are shown in the table.
Refer to Heart Rates and Exercise Narrative. Find the approximate p-value for the test in the previous question.

Question 60

In testing the hypotheses The two population locations are the same vs The location of population A is to the right of the location of population B, the statistics , , and are calculated with data drawn from a matched pairs experiment.
a. Which test is used in testing the hypotheses above?
b. What is the value of the test statistic?
c. What is the p-value of this test?
d. Can we infer at the 1% significance level that the location of population A is to the right of the location of population B? Explain.

Question 61

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. State the null and alternative hypotheses.

Question 62

Children and Antibiotics Narrative
In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm.
Antibiotic
Refer to Children and Antibiotics Narrative. Use the appropriate nonparametric test to test for differences in the distributions of responses to the tastes of the four antibiotics.

Question 63

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. What experimental design is being used in this ?

Question 64

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. Find the rejection region for = 0.05.

Question 65

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. Is there a difference among the population distributions of reaction times? Justify your answer.

Question 66

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.
Refer to Teaching Methods Narrative. Describe what the test statistic is. What is the value of in this ?

Question 67

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. What is the p-value for this ?

Question 68

A randomized block design is used to compare three treatments in six blocks.
Treatment
a. Use the Friedman test to detect differences in location among the three treatment distributions. Test using = 0.05.
b. Find the approximate p-value for the test in (a).
c. Perform an analysis of variance and give the ANOVA table for the analysis, and using statistical software to approximate the p-value for the F-statistic in testing the equality of the three treatment means. Test using = 0.05.
d. Compare the p-values for the tests in (b) and (c).

Question 69

Frozen TV Dinner Narrative
The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below.
Taste Ratings
Refer to Frozen TV Dinner Narrative. Which statistical technique can the general manager use to help him make a decision?

Question 70

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.
Refer to Teaching Methods Narrative. What is the observed significance level of this test?

Question 71

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.
Refer to Teaching Methods Narrative. What experimental design did the statistician use?

Question 72

Children and Antibiotics Narrative
In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm.
Antibiotic
Refer to Children and Antibiotics Narrative. What design is used in collecting these data?

Question 73

Frozen TV Dinner Narrative
The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market. He decides to perform an experiment to help make a decision. Each dinner is sampled by ten people who then rate the product on a 7-point scale, where 1 = poor, and 7 = excellent. The results are shown below.
Taste Ratings
Refer to Frozen TV Dinner Narrative. Can the general manager infer at the 5% significance level that there are differences in the taste ratings of the four dinners? Justify your decision.

Question 74

Children and Antibiotics Narrative
In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm.
Antibiotic
Refer to Children and Antibiotics Narrative. Using an appropriate statistical package for a two-way classification, produce a normal probability plot of the residuals as well as a plot of residuals vs. antibiotics. Do the usual analysis of variance assumptions appear to be satisfied? Report the ANOVA results.

Question 75

Children and Antibiotics Narrative
In a study of the palatability of antibiotics in children, a medical team used a voluntary sample of healthy children to assess their reactions to the taste of four antibiotics. The children's response was measured on a 10 centimetre (cm) visual analogue scale incorporating the use of faces, from sad (low score) to happy (high score). The minimum score was 0 and the maximum was 10. For the accompanying data, each of five children was asked to taste each of four antibiotics and rate them using the visual (faces) analogue scale from 0 to 10 cm.
Antibiotic
Refer to Children and Antibiotics Narrative. Comment on the results of the analysis of variance compared with the nonparametric test.

Question 76

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.

-Refer to Teaching Methods Narrative. Find the rejection region for $\alpha$ = 0.05.

Question 77

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.
Refer to Teaching Methods Narrative. State the null and alternative hypotheses.

Question 78

Teaching Methods Narrative
Two different workbooks and two distinct teaching machines were to be evaluated on their effectiveness in teaching the concept of multiplication. A Grade 4 class of 24 subjects was randomly assigned to 4 groups, and each group in turn was randomly assigned to a teaching method. A test was given and the number of errors was recorded. This uses the Kruskal-Wallis H test to see if the number of errors differs from one teaching method to another.
Refer to Teaching Methods Narrative. Can we conclude the teaching methods are equally effective? Explain.

Question 79

A toy store manager was interested in determining whether the assembly time is the same for three models of baby strollers. The manager selected five employees at random and asked each of them to assemble each of the strollers. The assembly time, in minutes, was recorded as follows: The manager wasn't sure whether the assumptions for the usual analysis of variance were valid, so she decided to use a nonparametric procedure. Use the appropriate method to determine whether the assembly time is the same for the three models of baby strollers. Use = 0.05.

Question 80

Reaction Times Narrative
The reaction times to three stimuli were recorded for each of eight subjects. The data, recorded in seconds, are shown below. This uses Friedman's F_r test to determine if there is a difference among the population distributions of reaction times.
Refer to Reaction Times Narrative. Describe what the test statistic is. What is the value of in this ?