Exam 16: Analysis of Variance

Use the following information for questions: An experiment is conducted to compare the enthusiasm of participants performing two different tasks. Before starting the task, the personality type of the participants is determined. Two groups are then formed: one group of personality type A people and an equal size group of personality type B people. There were more type A people in the initial sample, so they were randomly sampled until the right number was reached. Then half of the participants in each group was given one of two tasks. The one task is easy and earns the participants $1. The other task is difficult and earns the participant $10. Part of the computer output is shown below. -What are the results of this two-way ANOVA?

Use the following information for questions: Eighty-one 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. The surveyor records the gender of the customer on the survey as well. A two-way ANOVA is used to compare the mean amounts spent in the store between the four groups defined by the type of coupons the customers used and between genders. The SPSS output is provided below. -The profile plot given below was obtained from these data. What feature of this profile plot may have led you to come to the same conclusion as you did in question 91?

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)?

Use the following information for questions: Satisfaction scores are to be compared for women in five different treatment groups. Some sort of exercise is added to the daily routine of half of the women in each group. The other half of the women does not exercise. SPSS is used to compare the scores, not only between the five treatment groups, but also between the two exercise routines. -Is the interaction between treatment and exercise significant in this model? (Use $\alpha$ = 0.05)

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

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

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?

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?

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?

Use the following information for questions: 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?

Use the following information for questions: Satisfaction scores are to be compared for women in five different treatment groups. Some sort of exercise is added to the daily routine of half of the women in each group. The other half of the women does not exercise. SPSS is used to compare the scores, not only between the five treatment groups, but also between the two exercise routines. -How many women participated in this experiment?

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?

Use the following information for questions: 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?

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 for six babies born in each of the months January, May and September. Parents indicated how old (in weeks) their baby was when they first started crawling (not scooting on the belly). The researcher has elected to conduct Mood's median test to analyze the results. Computer output is shown below: -What is the null hypothesis for this test?

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

Use the following information for questions: 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?

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)?

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

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)?

Use the following information for questions: Satisfaction scores are to be compared for women in five different treatment groups. Some sort of exercise is added to the daily routine of half of the women in each group. The other half of the women does not exercise. SPSS is used to compare the scores, not only between the five treatment groups, but also between the two exercise routines. -What is the value of the SS Error?