Exam 12: Analysis of Variance

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 a significance level of 0.01.

A hotel chain has four hotels in Oregon. The general manager is interested in determining whether the mean length of stay is the same or different for the four hotels. She selects a random sample of n = 20 guests at each hotel and determines the number of nights they stayed. Assuming that she plans to test this using an alpha level equal to 0.05, which of the following is the appropriate alternative hypothesis?

A study recently conducted by a marketing firm analyzed three different advertising designs and four different income levels of potential customers. At each combination of factor A and factor B, 5 customers are observed and the number of products produced are recorded. The degrees of freedom for the MSE in this two-factor ANOVA design is 48.

A fast food chain operation is interested in determining whether the mean per customer purchase differs by day of the week. To test this, it has selected random samples of customers for each day of the week. The analysts then ran a one-way analysis of variance generating the following output: ANOVA: Single Factor Based upon this output, which of the following statements is true if the test is conducted at the 0.05 level of significance?

In conjunction with the housing foreclosure crisis of 2009, many economists expressed increasing concern about the level of credit card debt and efforts of banks to raise interest rates on these cards. The banks claimed the increases were justified. A Senate subcommittee decided to determine if the average credit card balance depends on the type of credit card used. Under consideration are Visa, MasterCard, Discover, and American Express. The sample sizes to be used for each level are 25, 25, 26, and 23, respectively. State the number of degrees of freedom available for determining the total variation.

The term one-way analysis of variance refers to the fact that in conducting the test, there is only one way to set up the null and alternative hypotheses.

Considering the following printout for a two-factor ANOVA study, which of the following is the number of replications used?

A test is conducted to compare three different income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages. Ten different person's income tax returns are done by each of the three software packages and the time is recorded for each. Given this format and testing using an alpha level equal to 0.05, the critical value associated with the primary hypothesis test is:

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. Test to determine if blocking the week on which the testing was done was necessary. Use a significance level of 0.05.

In a local community there are three grocery chain stores. The three have been carrying out a spirited advertising campaign in which each claims to have the lowest prices. A local news station recently sent a reporter to the three stores to check prices on several items. She found that for certain items each store had the lowest price. This survey didn't really answer the question for consumers. Thus, the station set up a test in which 20 shoppers were given different lists of grocery items and were sent to each of the three chain stores. The sales receipts from each of the three stores are recorded in the data file Groceries. Based on these sample data, can you conclude the three grocery stores have different sample means? Test using a significance level of 0.05. Use a p-value approach.

The following sample data were recently collected in the course of conducting a randomized block analysis of variance. Based on these sample data, what conclusions should be reached about blocking effectiveness and about the means of the three populations involved? Test using a significance level equal to 0.05.

Damage to homes caused by burst piping can be expensive to repair. By the time the leak is discovered, hundreds of gallons of water may have already flooded the home. Automatic shutoff valves can prevent extensive water damage from plumbing failures. The valves contain sensors that cut off water flow in the event of a leak, thereby preventing flooding. One important characteristic is the time (in milliseconds) required for the sensor to detect the water leak. Sample data obtained for four different shutoff valves are contained in the file entitled Waterflow. Produce the relevant ANOVA table and conduct a hypothesis test to determine if the mean detection time differs among the four shutoff valve models. Use a significance level of 0.05.

In a two-factor ANOVA design with replications, there are three hypotheses to be tested; test for factor A, test for factor B, and test for interaction between factors A and B.

An advertising company is interested in determining if there is a difference in the mean sales that will be generated for a soft drink company based on which shelf the soft drinks are located. There are four possible shelf levels. The ad company wants to control for store size. The following data reflect the sales for one week at each combination of shelf level and store size. Based on the experimental design, the calculated F-test statistic value for testing whether blocking on store size was effective is approximately 16.3.

Recently, a department store chain was interested in determining if there was a difference in the mean number of customers who enter the three stores in Seattle. The analysts set up a study in which the number of people entering the stores was counted depending on whether the day of the week was Saturday, Sunday, or a weekday. The following data were collected: Given this format, which of the following is true?

Consider the following: Test to determine whether blocking is effective using an alpha level equal to 0.05

Recently, a department store chain was interested in determining if there was a difference in the mean number of customers who enter the three stores in Seattle. The analysts set up a study in which the number of people entering the stores was counted depending on whether the day of the week was Saturday, Sunday, or a weekday. The following data were collected: Given this format and testing using an alpha level equal to 0.05, which of the following statements is true?

A large orchard owner in the state of Washington is interested in determining whether the mean number of bushels of peaches per acre is the same or different depending on the type of tree that is used. He also thinks that production may be affected by the type of fertilizer that is used. To test, he has set up a test in which a one-acre plot of peach trees with a combination each of 5 varieties and 3 fertilizer types are studied. In this case, the number of treatments is:

Given the partially completed ANOVA table below, the test statistic for determining if there is any blocking effect is F = 4.38.

In a randomized complete block design analysis of variance, which of the following correctly describes the number of degrees of freedom associated with the between sum of squares?