Exam 16: Analysis of Variance

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.

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:

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?

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 conclusion, using $\alpha$ = 0.05?

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. -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.

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 is the value of the test statistic for the interaction effect?

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)?

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)?

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

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 p-value?

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 test statistic for testing the interaction between treatment and exercise?

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)?

Using a sample of 300 children aged 10 to 12 years old, a child psychologist examines how scores on a "violent behaviors" index relate to gender and amount of television watching per day (less than 2 hours, 2 to 4 hours, more than 4 hours). In his report, the psychologist writes, "The effect of the amount of television watching on the violent behaviors index was more pronounced for males than for females." The sentence quoted in the previous sentence indicates that

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

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. -Refer to the profile plot given in problem 81. What feature of this profile plot tells us that there is a main effect due to batch?

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. -How many bottles of shampoo were sampled in total?

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?

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?

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?

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