Question 1

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

Accepted Answer

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. 
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 2

Use the following information for questions:
Fifty-five customers of a large-chain grocery store are asked to fill out an in-store survey. One of the questions on the survey asks about the use of coupons, while another question asks how much money the customer spent on groceries during that specific trip. Mood's median test is used to compare the median amounts spent in the store for four groups defined by the type of coupons the customers used. The categories were 'no coupons', 'coupons from the newspaper', coupons from the store's weekly flyer', and 'both types of coupons'. The SPSS output is provided below.
  
-What is the p-value?

Accepted Answer

The answer of Use the following information for questions:
Fifty-five customers...

Question 3

Use the following information for questions:
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.

Accepted Answer

H₀: μ₁ = μ₂ = μ₃ versus H_a: At least one popu

Question 4

Use the following information for questions:
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?

Accepted Answer

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. 
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 5

Use the following information for questions:
At a soap and shampoo factory, employees work in three different shifts: morning, evening, and night. At the shampoo production line, each shift produces six batches of shampoo. The quality control inspector wishes to compare the pH level of the shampoo between the different shifts and between the different batches. Several bottles of shampoo are randomly selected from each batch during each shift. The SPSS output is provided below.  
-The profile plot given below was obtained from these data. What feature of this profile plot tells us that there is a main effect due to shift?

Accepted Answer

The three different lines representing t

Question 6

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?

Accepted Answer

Mean Squar

Question 7

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

Accepted Answer

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

Question 8

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

Accepted Answer

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. 
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 9

Use the following information for questions:
 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.

Accepted Answer

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. 
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 10

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?

Accepted Answer

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. 
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 11

Use the following information for questions:
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?

Accepted Answer

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. 
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 12

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.

Accepted Answer

The answer of Use the following information for questions:
A researcher...

Question 13

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.

Accepted Answer

The null hypothesis is rejecte

Question 14

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

Accepted Answer

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 
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 15

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} $) ?

Accepted Answer

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

Question 16

Use the following information for questions:
 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.

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 17

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?

Accepted Answer

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

Question 18

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)?

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Use the following information for questions:
At a soap and shampoo factory, employees work in three different shifts: morning, evening, and night. At the shampoo production line, each shift produces six batches of shampoo. The quality control inspector wishes to compare the pH level of the shampoo between the different shifts and between the different batches. Several bottles of shampoo are randomly selected from each batch during each shift. The SPSS output is provided below.  
-According to the SPSS output the interaction between batch and shift ________ significant.

Accepted Answer

A)  is 
B)  is not 
A)  is 
B)  is not

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

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

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

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

Statistics Success Stories and Cautionary Tales

Turning Data Into Information

Relationships Between Quantitative Variables

Relationships Between Categorical Variables

Sampling: Surveys and How to Ask Questions

Gathering Useful Data for Examining Relationships

Probability

Random Variables

Understanding Sampling Distributions: Statistics As Random Variables

Estimating Proportions With Confidence

Estimating Means With Confidence

Testing Hypotheses About Proportions

Testing Hypotheses About Means

Inference About Simple Regression

More About Inference for Categorical Variables

Turning Information Into Wisdom

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Exam 16: Analysis of Variance

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

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

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

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

Statistics Success Stories and Cautionary Tales

Turning Data Into Information

Relationships Between Quantitative Variables

Relationships Between Categorical Variables

Sampling: Surveys and How to Ask Questions

Gathering Useful Data for Examining Relationships

Probability

Random Variables

Understanding Sampling Distributions: Statistics As Random Variables

Estimating Proportions With Confidence

Estimating Means With Confidence

Testing Hypotheses About Proportions

Testing Hypotheses About Means

Inference About Simple Regression

More About Inference for Categorical Variables

Turning Information Into Wisdom

Filters