Exam 12: Analysis of Variance

A test is conducted to compare three difference 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 people's income tax returns are done by each of the three software packages and the time is recorded for each.The computer results are shown below. Based on these results and using a 0.05 level of significance which is correct regarding blocking?

A study recently conducted by a marketing firm analyzed three different advertising designs (factor A)and four different income levels (factor B)of potential customers.At each combination of factor A and factor B,5 customers are observed and the number of products produced is recorded.Interaction between the two factors would exist if low income customers have higher mean buying when design 1 is used,but higher income customers have higher mean buying when designs 2 and 3 are used.

In comparing the average price of gasoline in 4 different cities,it is desired to check the assumption of equal variances using the Hartley test. The value of the test statistic for the Hartley test is:

In a two-factor ANOVA design,the variances of the populations are assumed to be equal unless there is interaction present.

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.

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.The managers are mainly interested in determining whether the mean strength is the same at all temperature settings,but they know that controlling for process time is important.The following data were observed from the experiment: Based on these data and experimental design,the primary null hypothesis to be tested is : = = .

In conducing one-way analysis of variance,the population distributions are assumed normally distributed.

Considering the following printout from a two-factor ANOVA design,how many levels of factor A (Sample)were there in this study?

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 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.

The one-way ANOVA test involves assuming that the population variances are equal.

In a recent one-way ANOVA test,SSW was equal to 15,900 and the SSB was equal to 3,100.Therefore,SST is equal to 12,800.

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?

To test the mileage efficiency of three new car models,random samples of various sample sizes were selected from each of the three cars and the mpg data obtained are shown below. Based on the sample date,one can conclude that

In conducting a one-way analysis of variance,if the null hypothesis is true then the variance between groups (MSB)should be approximately equal to the variance within groups (MSW).

In a randomized complete block design analysis of variance,how many factors are there to be analyzed?

In a one-way analysis of variance design,there is a single factor of interest but there may be multiple levels of the factor.