Exam 12: Analysis of Variance

Respond to the following questions using this partially completed one-way ANOVA table: How many different populations are being considered in this analysis?

A study has been conducted to determine whether the mean spending for recreational activities during the month of August differs for residents of three cities. Random samples of 30 people were selected from each city and their spending on recreation was recorded during August. The following output was generated using Excel: ANOVA: Single Factor Based on the information provided, should we conclude that the three populations (cities) have equal mean spending during August? Test at the 0.05 level of significance.

Which of the following is NOT one of the assumptions required by the randomized block design?

Consider the following: Test the main hypothesis of interest using α = 0.05

In a two-factor ANOVA design with replication, if the null hypothesis pertaining to interaction between factors A and B is rejected, then it is recommended that the hypothesis tests for factor A and factor B individually should not be conducted because the conclusions might be misleading.

In a two-factor ANOVA, the minimum number of replications required in any cell is two, but all cells must have the same number of replications.

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 the brands of shoes differ are D1 = 9 and D2 = 2.

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 number of treatments is two.

Explain what is meant by partitioning the sum of squares in a one-way analysis of variance application.

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 the sample data, which store has the highest average prices? Use Fisher's LSD test if appropriate.

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 managers should conclude that they were justified in blocking on store size if they test using a 0.05 level of significance.

An Internet service provider is interested in testing to see if there is a difference in the mean weekly connect time for users who come into the service through a dial-up line, DSL, or cable Internet. To test this, the ISP has selected random samples from each category of user and recorded the connect time during a week period. The following data were collected: Which of the following would be the correct alternative hypotheses for the test to be conducted?

Which of the following is the minimum number of required replications per cell for a two-factor ANOVA design if you plan to test for interactive effects between factors A and B?

In a two-factor ANOVA with replication in which all hypotheses are to be tested using an alpha = .05 level, if the p-value for interaction is .03467, the decision maker should conclude that no interaction is present.

Examine the following two-factor analysis of variance table: Complete the analysis of variance table.

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 total number of degrees of freedom associated with this two-factor ANOVA design is 59.

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 the design of this study, how many degrees of freedom will be associated with the mean square for factor A?

A two-factor analysis of variance is conducted to test the effect the price and advertising have on sales of a particular brand of bottled water. Each week a combination of particular levels of price and advertising are used and the sales level is recorded. The computer results are shown below. Based on the results above, which of the following is correct?

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 total number of degrees of freedom is 71.

If the null hypothesis that all population means are equal is rejected by the analysis of variance F-test, the alternative hypothesis that all population means differ is concluded to be true.