Exam 12: Analysis of Variance

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.

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:

The within sample variation is the dispersion that exists because the sample means for the various factor levels are not all equal.

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. Use the Tukey-Kramer multiple comparison technique to discover any differences in the average detection time.Use a significance level of 0.05.

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?

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:

Under what circumstances would you use a randomized complete block analysis of variance design instead of a one-way analysis of variance?

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 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: Based on the study's findings,was it correct to block for differences in textbooks? Conduct the appropriate test at the alpha = 0.10 level of significance.

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 experiment-wide error rate will be higher than the 0.05 significance level if the multiple comparison tests for the mean difference between any two populations use the 0.05 level.

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.

In a two-factor ANOVA design with replication,the null hypothesis for testing whether interaction exists is that no interaction exists.The alternative hypothesis is that interaction does exist.

In one-way analysis of variance,the within-sample variation is not affected by whether the null hypothesis is true or not.

A company has established an experiment with its production process in which three temperature settings are used and five elapsed times are used for each setting.The company then produces one product under each and measures the resulting strength of the product.This experimental design is called a randomized complete block design.

Explain what is meant by interaction between two factors in a two-way analysis of variance study.

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,what is the null hypothesis for testing whether blocking is effective?

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?

Under the basic logic of one-way analysis of variance,if the within variation is large relative to the between variation,it is an indication that the population means are likely to be different.

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