Deck 16: Analysis of Variance

Question 1

Which of the following is not one of the assumptions made in the analysis of variance?

A) Each sample is an independent random sample.
B) The distribution of the response variable is a normal curve within each population.
C) The different populations all have the same mean.
D) The different populations all have the same standard deviation $\sigma$ .

Answer 1

The different populations all have the same mean.

Question 2

Which one of the following choices describes a problem for which an analysis of variance would be appropriate?

A) Comparing the proportion of successes for three different treatments of anxiety. Each treatment is tried on 100 patients.
B) Analyzing the relationship between high school GPA and college GPA.
C) Comparing the mean birth weights of newborn babies for three different racial groups.
D) Analyzing the relationship between gender and opinion about capital punishment (favor or oppose).

Answer 2

Comparing the mean birth weights of newborn babies for three different racial groups.

Question 3

What procedure is used to test whether or not three or more population means are equal?

A) Analysis of correlation
B) 3-sample t-test
C) Chi-square test
D) Analysis of variance F-test

Answer 3

Analysis of variance F-test

Question 4

Which of the following is a research question that could be addressed using a one-way analysis of variance?

A) Does mean blood pressure differ for three different age groups?
B) Does the variance of blood pressure differ for three different age groups?
C) Are the proportions of people who oppose capital punishment different for three different age groups?
D) Is there a relationship between political party preference and age?

Question 5

Which of these situations could be analyzed with a one-way analysis of variance?

A) The relationship between gender (male or female) and opinion about the death penalty (favor, oppose, uncertain)
B) The relationship between weight and height for 12-year old girls
C) A comparison of four different age groups with regard to mean hours of watching television per day
D) A comparison of four different age groups with regard to proportion that opposes legalization of marijuana

Question 6

Ninety people with high cholesterol are randomly divided into three groups of thirty, and a different treatment program for decreasing cholesterol is assigned to each group. The response variable is the change in cholesterol level after two months of treatment. An analysis of variance will be used to compare the three treatments. What null hypothesis is tested by this F-test?

A) The sample variances are equal for the three treatment groups.
B) The population variances are equal for the three treatments.
C) The sample means are equal for the three treatment groups.
D) The population means are equal for the three treatments

Question 7

A one-way analysis of variance will be done to compare systolic blood pressures in three different age groups. What is the correct statement of the null hypothesis?

A)
B)
C)
D)

Question 8

Which of the following statements is not true about the F-test in one-way analysis of variance?

A) The F-statistic can never be a negative number.
B) The numerator degrees of freedom = number of groups in the study - 1
C) The denominator degrees of freedom = total sample size - number of groups.
D) An F-distribution is a symmetric distribution.

Question 9

Use the following information for questions:
A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets.

-What is the null hypothesis for this situation?

A) The average waiting time to check out is 25 minutes for all five supermarkets.
B) The average waiting time to check out is the same for all five supermarkets.
C) The average waiting time for each of the 100 shoppers is different.
D) The average waiting time to check out is not the same for all five supermarkets.

Question 10

Use the following information for questions:
A shopper wanted to test whether there was a difference in the average waiting times at the check-out counter among 5 different supermarkets. She selected a random sample of 20 shoppers from each of the five supermarkets.

-What is the alternative hypothesis for this situation?

A) The average waiting time to check out is 25 minutes for all five supermarkets.
B) The average waiting time to check out is the same for all five supermarkets.
C) The average waiting time for each of the 100 shoppers is different.
D) The average waiting time to check out is not the same for all five supermarkets.

Question 11

Use the following information for questions:
A student wanted to test whether there was a difference in the mean daily hours of study for students living in four different dormitories. She selected a random sample of 50 students from each of the four dormitories.

-What is the null hypothesis for this situation?

A) The mean daily hours of study is 3 hours for each dormitory.
B) The mean daily hours of study is the same for each dormitory.
C) The mean daily hours of study is different for each of the 200 students in the sample.
D) The mean daily hours of study is not the same for all four dormitories.

Question 12

Use the following information for questions:
A student wanted to test whether there was a difference in the mean daily hours of study for students living in four different dormitories. She selected a random sample of 50 students from each of the four dormitories.

-What is the alternative hypothesis for this situation?

A) The mean daily hours of study is 3 hours for each dormitory.
B) The mean daily hours of study is the same for each dormitory.
C) The mean daily hours of study is different for each of the 200 students in the sample.
D) The mean daily hours of study is not the same for all four dormitories.

Question 13

When multiple tests are done in analysis of variance, the family error rate is

A) the smallest p-value among the tests in the set.
B) the probability of making one or more type 2 errors among the tests.
C) the probability of not rejecting the null hypothesis when the null hypothesis is true.
D) the probability of making one or more type 1 errors among the tests.

Question 14

A sample of students was asked where they typically sat in their statistics class (back, middle, and front). An analysis of variance using y = height (inches) versus typical seating was done. Minitab results for the Tukey method of multiple comparisons using a family error rate of 0.05 are shown below. Based on these results, which (if any) pair wise differences are statistically significant?

A) None of the differences are statistically significant.
B) All three differences are statistically significant.
C) Only the difference between the back versus front is statistically significant.
D) Both the difference between back versus middle and middle versus front are statistically significant.

Question 15

Use the following information for questions:
A company that owns five resort hotels wants to compare guest satisfaction across the hotels. For each hotel, the company's research department randomly sampled 21 people who had stayed at the hotel during the past month and asked them to rate their expectation of the hotel before their stay and to rate the quality of their actual stay at the hotel. Both observations used a rating scale of 0 to 10 with 0 = "very poor" and 10 = "excellent". For each guest, the researchers calculated a performance gap score, defined as the difference between a guest's prior expectation rating and actual quality rating.
-Identify the response variable and the explanatory variable.

Question 16

Use the following information for questions:
A company that owns five resort hotels wants to compare guest satisfaction across the hotels. For each hotel, the company's research department randomly sampled 21 people who had stayed at the hotel during the past month and asked them to rate their expectation of the hotel before their stay and to rate the quality of their actual stay at the hotel. Both observations used a rating scale of 0 to 10 with 0 = "very poor" and 10 = "excellent". For each guest, the researchers calculated a performance gap score, defined as the difference between a guest's prior expectation rating and actual quality rating.
-How many guests were in the study?

Question 17

Use the following information for questions:
A company that owns five resort hotels wants to compare guest satisfaction across the hotels. For each hotel, the company's research department randomly sampled 21 people who had stayed at the hotel during the past month and asked them to rate their expectation of the hotel before their stay and to rate the quality of their actual stay at the hotel. Both observations used a rating scale of 0 to 10 with 0 = "very poor" and 10 = "excellent". For each guest, the researchers calculated a performance gap score, defined as the difference between a guest's prior expectation rating and actual quality rating.
-What are the degrees of freedom of the F-distribution if we were to use an ANOVA to compare the population means?

Question 18

Use the following information for questions:
A company that owns five resort hotels wants to compare guest satisfaction across the hotels. For each hotel, the company's research department randomly sampled 21 people who had stayed at the hotel during the past month and asked them to rate their expectation of the hotel before their stay and to rate the quality of their actual stay at the hotel. Both observations used a rating scale of 0 to 10 with 0 = "very poor" and 10 = "excellent". For each guest, the researchers calculated a performance gap score, defined as the difference between a guest's prior expectation rating and actual quality rating.
-Suppose the F-statistic for comparing the five means is F = 4.5. What can you say about the corresponding p-value?

Question 19

In a one-way analysis of variance, the "Sum of Squares for Groups" is a measure of the

A) variation among observed sample standard deviations
B) variation among observed sample sizes
C) variation among observed sample means
D) variation among individuals within a group

Question 20

In a one-way analysis of variance, the "Sum of Squared Errors" is a measure of the

A) variation among population means
B) variation among individuals within groups
C) variation among observed sample means
D) variation among sample sizes

Question 21

When a one-way analysis of variance test is done, what probability distribution is used to find the p-value?

A) F-distribution
B) normal distribution
C) Chi-square distribution
D) t-distribution

Question 22

Use the following information for questions:
A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

-What are the numerator and denominator degrees of freedom for the F-test?

A) 10 for numerator and 30 for denominator.
B) 3 for numerator and 29 for denominator.
C) 3 for numerator and 26 for denominator.
D) None of the above.

Question 23

Use the following information for questions:
A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

-The sum of squared errors is SS Error = 100. What is the value of the Mean Square Error (MS Error)?

A) 10
B) 3.45
C) 3.85
D) None of the above.

Question 24

Use the following information for questions:
A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

-The sum of squares for groups is SS Groups = 60. What is the Mean Square for groups (MS Groups)?

A) 15
B) 20
C) 60
D) None of the above.

Question 25

Use the following information for questions:
A study compared testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. The total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo). A one-way analysis of variance was used to compare the population mean levels for the four sports.

-The p-value for the F-test is = 0.02. Using the $\alpha$ = 0.05 significance level, what is the conclusion?

A) The null hypothesis is not rejected: the means are not significantly different.
B) The null hypothesis is not rejected: the means are significantly different.
C) The null hypothesis is rejected: the means are not significantly different.
D) The null hypothesis is rejected: the means are significantly different.

Question 26

Use the following information for questions:
A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance.

-What are the numerator and denominator degrees of freedom for the F-test?

A) 6 for numerator and 12 for denominator.
B) 5 for numerator and 11 for denominator.
C) 5 for numerator and 6 for denominator.
D) None of the above.

Question 27

Use the following information for questions:
A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance.

-The Error Sum of Squares is SS Error = 50. What is the Mean Square Error (MS Error)?

A) 4.17
B) 8.33
C) 10.00
D) None of the above.

Question 28

Use the following information for questions:
A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance.

-The sum of squares for groups is SS Groups = 60. What is the Mean Square for groups (MS Groups)?

A) 10
B) 12
C) 30
D) None of the above.

Question 29

Use the following information for questions:
A study compared grade point averages (GPA) for students in a class: students were divided by 6 locations where they usually sat during lecture (i.e. left or right front, left or right center, left or right rear). A total sample size of 12 students was studied (2 students from each section) using one-way analysis of variance.

-The p-value for the F-test is 0.46. If the significance level = 0.05, what is the conclusion?

A) The null hypothesis is not rejected so we cannot say the population means are different.
B) The null hypothesis is not rejected so we can say the population means are different.
C) The null hypothesis is rejected so we cannot say the population means are different.
D) The null hypothesis is rejected so we can say the population means are different.

Question 30

Use the following information for questions:
A study compared grade point averages (GPA) among students in 4 different majors (English, History, Statistics, and Art) using analysis of variance. A total sample size of 20 students (5 in each major) was studied.

-What are the numerator and denominator degrees of freedom for the F-test?

A) 5 for numerator and 20 for denominator.
B) 4 for numerator and 79 for denominator.
C) 3 for numerator and 16 for denominator.
D) None of the above.

Question 31

Use the following information for questions:
A study compared grade point averages (GPA) among students in 4 different majors (English, History, Statistics, and Art) using analysis of variance. A total sample size of 20 students (5 in each major) was studied.

-The Error Sum of Squares is SS Error = 64. What is the Mean Square Error (MS Error)?

A) 3.2
B) 4
C) 16
D) None of the above.

Question 32

Use the following information for questions:
A study compared grade point averages (GPA) among students in 4 different majors (English, History, Statistics, and Art) using analysis of variance. A total sample size of 20 students (5 in each major) was studied.

-The sum of squares for groups is SS Groups = 60. What is the Mean Square for groups (MS Groups)?

A) 3
B) 15
C) 20
D) None of the above.

Question 33

Use the following information for questions:
A study compared grade point averages (GPA) among students in 4 different majors (English, History, Statistics, and Art) using analysis of variance. A total sample size of 20 students (5 in each major) was studied.

-The p-value for the F-test is 0.013. If the significance level = 0.05, what is the conclusion from the analysis of variance?

A) The null hypothesis is not rejected; the sample means are not significantly different.
B) The null hypothesis is not rejected; the sample means are significantly different.
C) The null hypothesis is rejected; the sample means are not significantly different.
D) The null hypothesis is rejected; the sample means are significantly different.

Question 34

Use the following information for questions:
A study compared weight loss among 5 different diet programs. A total sample size of 25 people was studied (5 people from each program) using one-way analysis of variance.

-What are the numerator and denominator degrees of freedom for the F-test?

A) 5 for numerator and 25 for denominator.
B) 5 for numerator and 24 for denominator.
C) 4 for numerator and 20 for denominator.
D) None of the above.

Question 35

Use the following information for questions:
A study compared weight loss among 5 different diet programs. A total sample size of 25 people was studied (5 people from each program) using one-way analysis of variance.

-The Error Sum of Squares is SS Error = 40. What is the Mean Square Error (MS Error)?

A) 2
B) 4
C) 8
D) None of the above.

Question 36

Use the following information for questions:
A study compared weight loss among 5 different diet programs. A total sample size of 25 people was studied (5 people from each program) using one-way analysis of variance.

-The sum of squares for groups is SS Groups = 80. What is the Mean Square for groups (MS Groups)?

A) 4
B) 5
C) 20
D) None of the above.

Question 37

Use the following information for questions:
A study compared weight loss among 5 different diet programs. A total sample size of 25 people was studied (5 people from each program) using one-way analysis of variance.

-The p-value of the F-test is 0.327. If the significance level = 0.05, what is the conclusion from the analysis of variance?

A) The null hypothesis is not rejected; the sample means are not significantly different.
B) The null hypothesis is not rejected; the sample means are significantly different.
C) The null hypothesis is rejected; the sample means are not significantly different.
D) The null hypothesis is rejected; the sample means are significantly different.

Question 38

Use the following information for questions:
Twenty students were randomly assigned to one of four exercise programs (5 students in each program), and the mean weight losses for the four programs were compared using one-way analysis of variance. The mean square error (MS Error) was 40. The mean weight loss for the first program was $\overline{x_1}$ = 5 pounds.

-What are the degrees of freedom for the t^* multiplier for a confidence interval for $µ_1$ the population mean weight loss for the first program

A) 3
B) 15
C) 16
D) 20

Question 39

Use the following information for questions:
Twenty students were randomly assigned to one of four exercise programs (5 students in each program), and the mean weight losses for the four programs were compared using one-way analysis of variance. The mean square error (MS Error) was 40. The mean weight loss for the first program was $\overline{x_1}$ = 5 pounds.

-What is the standard error of $\overline{x_1}$ , the sample mean weight loss in the first program?

A) 0.32
B) 1.41
C) 2.83
D) None of the above

Question 40

Use the following information for questions:
Twenty students were randomly assigned to one of four exercise programs (5 students in each program), and the mean weight losses for the four programs were compared using one-way analysis of variance. The mean square error (MS Error) was 40. The mean weight loss for the first program was $\overline{x_1}$ = 5 pounds.

-What is a 90% confidence interval for the mean weight loss from the first program?

A) (4.44, 5.56)
B) (2.53, 7.47)
C) (0.05, 9.95)
D) None of the above

Question 41

Use the following information for questions:
12 corn plants were randomly assigned to one of four plots of land (3 plants in each plot), and the mean heights of the plants were compared for the four plots using one-way analysis of variance. The mean square error (MS Error) was 20. The average height of the corn plants in the first plot was $\overline{x_1}$ = 60 inches.

-What are the degrees of freedom for the t^* multiplier for a confidence interval for $µ_1$ the average height of corn plants grown in the first plot?

A) 8
B) 12
C) 20
D) None of the above

Question 42

Use the following information for questions:
12 corn plants were randomly assigned to one of four plots of land (3 plants in each plot), and the mean heights of the plants were compared for the four plots using one-way analysis of variance. The mean square error (MS Error) was 20. The average height of the corn plants in the first plot was $\overline{x_1}$ = 60 inches.

-What is the standard error of the sample mean weight loss in the first program( $\overline{x_1}$ ) ?

A) 4.47
B) 1.73
C) 2.58
D) None of the above

Question 43

Use the following information for questions:
12 corn plants were randomly assigned to one of four plots of land (3 plants in each plot), and the mean heights of the plants were compared for the four plots using one-way analysis of variance. The mean square error (MS Error) was 20. The average height of the corn plants in the first plot was $\overline{x_1}$ = 60 inches.

-What is a 99% confidence interval for the mean weight loss from the first program?

A) (51.3, 68.7)
B) (54.2, 65.8)
C) (45.0, 75.0)
D) None of the above

Question 44

Use the following information for questions:
On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.


-If $µ_1$ , $µ_2$ and $µ_3$ are the population means of GPA for the about right, overweight and underweight groups, respectively, then the alternative hypotheses tested by this analysis is:

A) $µ_1$ , $µ_2$ and $µ_3$ are all different.
B) At least two of $µ_1$ , $µ_2$ and $µ_3$ are different from each other.
C) $µ_1$ = $µ_2$ ? $µ_3$
D) $µ_1$ > $µ_2$ > $µ_3$

Question 45

Use the following information for questions:
On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.


-The mean square for groups in this study is:

A) 2.134
B) 1.067
C) 49.719
D) 0.214

Question 46

Use the following information for questions:
On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.


-Assuming the population standard deviations are equal, the best estimate of the standard deviation of GPAs for the populations represented is:

A) 0.4305
B) 0.5461
C) 0.4505
D) 0.4629

Question 47

Use the following information for questions:
On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.


-The p-value of 0.008 is found by calculating:

A) the area to the right of 4.98 under an F-distribution with 2 and 232 degrees of freedom.
B) the area to the right of 4.98 under an F-distribution with 2 and 234 degrees of freedom.
C) the area to the right of 4.98 and to the left of -4.98 under an F-distribution with 2 and 232 degrees of freedom.
D) the area to the right of 4.98 and to the left of -4.98 under an F-distribution with 2 and 234 degrees of freedom.

Question 48

Use the following information for questions:
On a survey conducted at a university, students were asked how they felt about their weight (about right, overweight, or underweight), and also were asked to record their grade point average (GPA). There were 234 responses, with 160 saying their weight was about right, 50 said they were overweight, and 17 underweight. The question of interest is whether mean GPA is the same or differs for different weight attitude populations. Minitab output for the study is given below.


-What is the appropriate conclusion to draw from this analysis?

A) If a student is underweight he (she) should gain weight in order to raise his (her) GPA.
B) Overweight students should go on a diet to lose weight because this will result in a higher GPA.
C) There is no significant difference among the mean GPAs of students in the three weight attitude groups.
D) There is a significant difference among the mean GPAs of students in the three weight attitude groups.

Question 49

Use the following information for questions:
Five different training programs for improving endurance are compared. Forty individuals are randomly divided into five groups of n = 8 each and a different training program is assigned to each group. After two months, the improvement in endurance is recorded for each participant.

-A one-way analysis of variance is used to compare the five training programs, and the resulting p-value is 0.023. At a significance level of 0.05, the appropriate conclusion about mean improvement in endurance is that it

A) is the same for the five training programs.
B) is different for each of the five training programs
C) differs for at least two of the five training programs.
D) is significantly better for one of the training programs than for the other four.

Question 50

Use the following information for questions:
Five different training programs for improving endurance are compared. Forty individuals are randomly divided into five groups of n = 8 each and a different training program is assigned to each group. After two months, the improvement in endurance is recorded for each participant.

-The p-value in this situation would be found using

A) an F-distribution with 39 degrees of freedom.
B) an F-distribution with 5 and 8 degrees of freedom.
C) an F-distribution with 4 and 3 degrees of freedom.
D) an F-distribution with 4 and 35 degrees of freedom.

Question 51

In a student survey, two of the questions asked are:
(1) How many times do you pray per month?
(2) What is the importance of religion in your life (fairly important, not very important, or very important)?
Descriptive statistics for the three different categories of the importance of religion are given in the following table.
To compare the times of praying for the three groups, an analysis of variance F-test

A) can be done because the sample means are unequal.
B) should not be done because the sample means are unequal.
C) should not be done because the sample standard deviations differ by so much.
D) can be done because the data probably have a normal distribution.

Question 52

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, an analysis of variance is done to compare the mean ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). Some Minitab output is shown below.
-State the null and alternative hypothesis for the analysis of variance.

Question 53

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, an analysis of variance is done to compare the mean ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). Some Minitab output is shown below.
-What are the degrees of freedom for the between groups factor (educational degree)?

Question 54

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, an analysis of variance is done to compare the mean ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). Some Minitab output is shown below.
-What is the value for the Mean Square Error?

Question 55

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, an analysis of variance is done to compare the mean ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). Some Minitab output is shown below.
-What is the p-value?

Question 56

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, an analysis of variance is done to compare the mean ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). Some Minitab output is shown below.
-For a significance level of 0.05, state a conclusion in the context of this situation.

Question 57

Use the following information for questions:
A researcher is hired by a company that sells appliances to investigate whether there is any difference in the average ratings that customers give to a DVD player between three different age groups. Sixty-eight people were asked to fill out a questionnaire and rate the DVD player by answering various questions (easy to use? looks nice? manual understandable?) after using it for a week. The scores (a value between 1 and 50) were recorded and a one-way ANOVA was performed. Partial SPSS output is provided below.
-One of the assumptions in ANOVA is that the standard deviation for the response (DVD assessment score) for each age group is the same. Give an estimate of that common standard deviation.

Question 58

Use the following information for questions:
A researcher is hired by a company that sells appliances to investigate whether there is any difference in the average ratings that customers give to a DVD player between three different age groups. Sixty-eight people were asked to fill out a questionnaire and rate the DVD player by answering various questions (easy to use? looks nice? manual understandable?) after using it for a week. The scores (a value between 1 and 50) were recorded and a one-way ANOVA was performed. Partial SPSS output is provided below.
-What is the numerical value of the test statistic that we would calculate to assess equality of the average DVD assessment scores for the three different age groups? Include the symbol we use to represent this test statistic in your answer.

Question 59

Use the following information for questions:
A researcher is hired by a company that sells appliances to investigate whether there is any difference in the average ratings that customers give to a DVD player between three different age groups. Sixty-eight people were asked to fill out a questionnaire and rate the DVD player by answering various questions (easy to use? looks nice? manual understandable?) after using it for a week. The scores (a value between 1 and 50) were recorded and a one-way ANOVA was performed. Partial SPSS output is provided below.
-Using a 5% significance level, what is the conclusion of the analysis of variance?

Question 60

Use the following information for questions:
A researcher is hired by a company that sells appliances to investigate whether there is any difference in the average ratings that customers give to a DVD player between three different age groups. Sixty-eight people were asked to fill out a questionnaire and rate the DVD player by answering various questions (easy to use? looks nice? manual understandable?) after using it for a week. The scores (a value between 1 and 50) were recorded and a one-way ANOVA was performed. Partial SPSS output is provided below.
-Which distribution was used to calculate the p-value of 0.000059? Include all details of this distribution.

Question 61

Use the following information for questions:
A researcher is hired by a company that sells appliances to investigate whether there is any difference in the average ratings that customers give to a DVD player between three different age groups. Sixty-eight people were asked to fill out a questionnaire and rate the DVD player by answering various questions (easy to use? looks nice? manual understandable?) after using it for a week. The scores (a value between 1 and 50) were recorded and a one-way ANOVA was performed. Partial SPSS output is provided below.
-Summary measures for the three groups are given below. Calculate a 95% confidence interval for the average DVD assessment score for the middle aged group.

Question 62

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A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and the concentration levels along with some summaries are provided below:
-Some values in the ANOVA table are missing. Complete the ANOVA table. Specifically show your work for finding the SSGroups (or SS Between Cities)

Question 63

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A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and the concentration levels along with some summaries are provided below:
-One of the assumptions in ANOVA is that the standard deviation for the response (sulfur dioxide concentrations) for each city population be the same. Give an estimate of that common standard deviation.

Question 64

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A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and the concentration levels along with some summaries are provided below:

-Suppose the necessary assumptions hold. Using a 10% significance level, which of the following is the correct conclusion?

A) It appears that the mean concentration levels are the same for the three city populations.
B) It appears that at least one of the population mean concentration levels is different.
C) It appears that the population mean concentration levels are all different.

Question 65

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A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and the concentration levels along with some summaries are provided below:

-Consider the following four statements. Clearly select all that are correct.

A) If this study were repeated many times, the null hypothesis would be true only 6.4% of the time.
B) If this study were repeated many times, we would see an F statistic as large as or larger than that observed in about 6.4% of the repetitions.
C) If this study were repeated many times and if the population means were all equal, we would see an F statistic as large as or larger than that observed in about 6.4% of the repetitions.
D) If this study were repeated many times and if the population means were all equal, we would reject the null hypothesis in about 10% of the repetitions.

Question 66

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A study was conducted to compare the mean sulfur dioxide concentrations for three cities. Independent random samples were obtained from each city and the concentration levels along with some summaries are provided below:
-Multiple comparisons output using Tukey's procedure is provided. Does there seem to be a difference between the average sulfur dioxide concentrations for City 1 versus City 2 at the 10% level? Explain your answer (include relevant numbers from the output)..

Question 67

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.

-State the null and alternative hypotheses for testing whether or not the training level has an effect on the mean time. Also include a description of the parameters of interest.

Question 68

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.

-The ANOVA table gives the F-statistic. What is the distribution of the F-statistic (if we assume that, on average, the time required to complete the task is the same across the three training level populations)?

Question 69

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.

-State your decision regarding the hypotheses in question 67 and give a corresponding conclusion in the context of the problem. Use a 5% significance level.

Question 70

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.

-One assumption in ANOVA is that the three populations have equal standard deviations. Using the sample standard deviations reported in the Descriptives output comment on this assumption.

Question 71

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.


-Multiple comparisons were performed using Tukey's procedure. The resulting table is given below Clearly select all pairs that are significantly different at the 5% level.

A) Beginning versus Intermediate
B) Intermediate versus Advanced
C) Beginning versus Advanced
D) None of the pairs show a significant difference.

Question 72

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A supervisor wants to study the relationship between employee training and time required to complete a job-related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results are given below.

-Provide a 99% confidence interval for the population mean time it takes to complete the task for all employees that receive beginner level training.

Question 73

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Ninety-four female students were asked how many hours of TV they watched the night before and where the usually sat in class (front, middle, back). A nonparametric Kruskal-Wallis test was used to analyze the results. Minitab output is shown below:

-What is the null hypothesis in this situation?

A) Population means for hours of TV watched are equal for the three populations.
B) Population means for hours of TV watched are not equal for the three populations.
C) Population medians for hours of TV watched are equal for the three populations.
D) Population medians for hours of TV watched are not equal for the three populations.

Question 74

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Ninety-four female students were asked how many hours of TV they watched the night before and where the usually sat in class (front, middle, back). A nonparametric Kruskal-Wallis test was used to analyze the results. Minitab output is shown below:

-Based on information given in the output, what is the conclusion, using a significance level of 0.05?

A) The null hypothesis is not rejected: the populations are not significantly different in TV hours watched.
B) The null hypothesis is not rejected: the populations are significantly different in TV hours watched.
C) The null hypothesis is rejected: the populations are not significantly different in TV hours watched.
D) The null hypothesis is rejected: the populations are significantly different in TV hours watched.

Question 75

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How old are babies when they learn how to crawl? Does it take longer in the winter months because of all the bulky clothes? Data was collected at various pediatricians' offices. Parents indicated how old (in weeks) their baby was when they first started crawling (not scooting on the belly). Data for babies born in January, May and September is displayed below.

-The researcher has elected to conduct a nonparametric Kruskal-Wallis test to analyze the results. What would be the correct null hypothesis for this test?

A) The sample means are equal for the three age groups.
B) The population medians for the three age groups all differ.
C) The sample medians are equal for the three age groups.
D) The population medians are equal for the three age groups.

Question 76

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How old are babies when they learn how to crawl? Does it take longer in the winter months because of all the bulky clothes? Data was collected at various pediatricians' offices. Parents indicated how old (in weeks) their baby was when they first started crawling (not scooting on the belly). Data for babies born in January, May and September is displayed below.

-The computer was used to analyze the data and the test statistic value was 3.82. At the 5% significance level, the critical value for this test is 5.99. What is the conclusion?

A) The results are significant and conclude that the median crawling ages appear to be equal for the three age group populations.
B) The results are not significant and conclude that the median crawling ages appear to be equal for the three age group populations.
C) The results are significant and conclude that the median crawling ages do not appear to be equal for the three age group populations.
D) The results are not significant and conclude that the median crawling ages do not appear to be equal for the three age group populations.

Question 77

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Did you wash your hands with soap before eating? You've undoubtedly been asked that question a few times in your life. Mom knows that washing with soap eliminates most of the germs you've managed to collect on your hands. Or does it? A student decided to investigate just how effective washing with soap is in eliminating bacteria. To do this she measured the bacterial count after using one of four different methods - washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with antibacterial spray (containing 65% ethanol as an active ingredient). SPSS output of the Kruskal-Wallis test is provided below.

-What is the null hypothesis in this situation?

A) The four population mean bacterial counts are equal for the four populations.
B) The four population mean bacterial counts are not equal for the four populations.
C) The four population median bacterial counts are equal for the four populations.
D) The four population median bacterial counts are not equal for the four populations.

Question 78

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Did you wash your hands with soap before eating? You've undoubtedly been asked that question a few times in your life. Mom knows that washing with soap eliminates most of the germs you've managed to collect on your hands. Or does it? A student decided to investigate just how effective washing with soap is in eliminating bacteria. To do this she measured the bacterial count after using one of four different methods - washing with water only, washing with regular soap, washing with antibacterial soap, and spraying hands with antibacterial spray (containing 65% ethanol as an active ingredient). SPSS output of the Kruskal-Wallis test is provided below.

-Based on information given in the output, what is the conclusion, using a significance level of 0.01?

A) The null hypothesis is not rejected: the population median bacterial counts after washing hands are not significantly different.
B) The null hypothesis is not rejected: the population median bacterial counts after washing hands are significantly different.
C) The null hypothesis is rejected: the population median bacterial counts after washing hands are not significantly different.
D) The null hypothesis is rejected: the population median bacterial counts after washing hands are significantly different.

Question 79

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Using data from 496 respondents in a past General Social Survey, a Kruskal-Wallis test is done to compare the median ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). The Minitab output is provided below.
-What is the null hypothesis in this situation?

Question 80

Use the following information for questions:
Using data from 496 respondents in a past General Social Survey, a Kruskal-Wallis test is done to compare the median ages in five populations defined by the highest educational degree received (no high school degree, high school degree, junior college, bachelor degree, graduate degree). The Minitab output is provided below.
-What is the alternative hypothesis in this situation?