Exam 12: Analysis of Variance

Applebee's International, Inc., is a U.S. company that develops, franchises, and operates the Applebee's Neighborhood Grill and Bar restaurant chain. It is the largest chain of casual dining restaurants in the country, with over 1,500 restaurants across the United States. The headquarters is located in Overland Park, Kansas. The company is interested in determining if mean weekly revenue differs among three restaurants in a particular city. The file entitled Applebees contains revenue data for a sample of weeks for each of the three locations. Based on the data gathered by Applebee's, can it be concluded that there is a difference in the average revenue among the three restaurants?

A car company is interested in testing to see whether the mean miles that a car engine will last without changing oil is the same or different depending on which brand of oil is used. The engineers also wish to control for the type of transmission (manual or automatic) that is used. To conduct this test, the car company obtains enough engines so that all four oil brands can be tested in a design that involves no replication. The following data reflect the miles the engine lasted until problems were encountered. Data are in thousands of miles. Assuming that the hypothesis tests are conducted using a significance level equal to 0.05, which of the following statements is true?

In a one-way ANOVA, which of the following is true?

Interaction is the term that is used in a two-factor ANOVA design when the two factors have different means.

A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Given this information, the correct null and alternative hypotheses are:

A marketing study was recently conducted to see whether the mean monthly sales for a department store located in four cities differ. A random sample of 6 months were selected from each store. Based upon this information, the appropriate null hypothesis to be tested is H0 : μ1 = μ2 = μ3 = μ4

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. The number of degrees of freedom in the interaction row of the ANOVA table is 15.

Recently, a company tested three different machine types to see if there was a difference in the mean thickness of products produced by the three. A random sample of ten products was selected from the output from each machine. Given this information, the proper design to test whether the means are equal is a one-way ANOVA balanced design.

A study was conducted to determine if differences in new textbook prices exist between on-campus bookstores, off-campus bookstores, and Internet bookstores. To control for differences in textbook prices that might exist across disciplines, the study randomly selected 12 textbooks and recorded the price of each of the 12 books at each of the three retailers. You may assume normality and equal-variance assumptions have been met. The partially completed ANOVA table based on the study's findings is shown here: Complete the ANOVA table by filling in the missing sums of squares, the degrees of freedom for each source, the mean square, and the calculated F-test statistic for each possible hypothesis test.

What are the assumptions for a one-way analysis of variance design?

In a completely randomized analysis of variance design, the observations from each factor are selected in an independent and random fashion.

Given the following sample data Based on the computations for the within- and between-sample variation, develop the ANOVA table and test the appropriate null hypothesis using alpha= 0.05. Use the p-value approach.

Six food critics each visited and rated four different restaurants. Each critic visited each restaurant on three separate occasions and recorded a score for each visit. Assume that results show that there is an interaction. This would mean that, for example, which restaurant is rated the highest depends on which critic does the rating.

A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following shows the results of the ANOVA computations. However, the degrees of freedom column has been omitted. The correct number of degrees of freedom for the within variation is 28.

In a one-way analysis of variance test in which the levels of the factor being analyzed are randomly selected from a large set of possible factors, the design is referred to as:

A golf ball manufacturer has three dimple patterns it is interested in analyzing to see whether one results in longer driving distances. However, it also wishes to control for the cover material the ball is made from since it believes that the material might affect driving distance. Four materials can be used. The following data represent the results of tests in which each combination of dimple pattern and cover material were used and the length of the ball hit by a robot has been recorded. The test will be conducted using an alpha = 0.05 level. Given these data, which of the following statements is true?

Respond to the following questions using this partially completed one-way ANOVA table: Based on the analysis of variance F-test, what conclusion should be reached regarding the null hypothesis? Test using alpha = 0.05.

Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The degrees of freedom for testing whether there is any blocking effect D1 = 9 and D2 = 18.

Three brands of running shoes are each tested by 10 different runners. The amount of wear on the sole of the shoes is then measured. The objective is to determine if there is any difference among the three brands of shoes based on how long the soles last. The null hypothesis is: H0 : μ1 = μ2 = μ3.

A national car rental company recently conducted a study recently in which cars with automatic and standard transmissions (factor A-Sample) were rented to male and female customers (factor B-Columns). Three customers in each category were randomly selected and the miles driven per day was recorded as follows: Based on these sample data, and alpha = .05, which of the following statements is true?