Exam 12: Analysis of Variance

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. If the test is to be conducted using an alpha = 0.05 level, the critical value will be F = 3.838.

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 a significance level of 0.05 and these sample data, test to determine whether blocking was necessary in this example. Use a test-statistic approach.

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. Which of the following is true?

A personal computer assembly company is interested in studying the time it takes to assemble a computer under different conditions. Specifically, two factors are to be controlled: Factor A (Sample) is the number of individual work stations in the line and Factor B (Columns) is whether the assembly was done on day shift, swing shift, or graveyard shift. The following data were obtained in the study where the response variable is the time required to assemble the PC from start to final test. Carry out the appropriate statistical tests using an alpha equal .05 level.

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.

Consider the following: How many blocks were used in this study?

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

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).

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. The following data reflect the number of bushels of peaches on each acre plot. Assuming that the hypothesis tests will be conducted using an alpha equal 0.05 level, which of the following is true?

In a two-factor ANOVA, the total sum of squares can be partitioned into four parts; the variation due to factor A, the variation due to factor B, the variation due to blocking, and the error variation.

A randomized complete block analysis of variance allows the analyst to control for sources of variation that might adversely affect the analysis by using the concept of paired samples.

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 chart shows some of the results of the ANOVA computations; however, some of the output is missing. Given what is available, the proper conclusion to reach based on the sample data is that the population means could be equal using a 0.05 level of significance.

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 persons' 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?

In a one-way analysis of variance design, the total variation in the data across the various factor levels can be partitioned into two parts, the within sample variation and the between sample variation.

The State Transportation Department is thinking of changing its speed limit signs. It is considering two new options in addition to the existing sign design. At question is whether the three sign designs will produce the same mean speed. To test this, the department has conducted a limited test in which a stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the following summary statistics were computed based on the data: Based on these sample results and a significance level equal to 0.05, assuming that the null hypothesis of equal means has been rejected, the Tukey-Kramer critical range is:

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, can it be concluded that there is a difference in the average price of textbooks across the three retail outlets? Conduct the appropriate hypothesis test at the alpha = 0.10 level of significance.

Based on the partially completed ANOVA table below, we know that 3 samples are being compared using 9 blocks.

The State Transportation Department is thinking of changing its speed limit signs. It is considering two new options in addition to the existing sign design. At question is whether the three sign designs will produce the same mean speed. To test this, the department has conducted a limited test in which a stretch of roadway was selected. With the original signs up, a random sample of 30 cars was selected and the speeds were measured. Then, on different days, the two new designs were installed, 30 cars each day were sampled, and their speeds were recorded. Suppose that the following summary statistics were computed based on the data: Based on these sample results and significance level equal to 0.05, the sum of squares between is:

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

Examine the following two-factor analysis of variance table: Does the ANOVA table indicate that the levels of factor B have equal means? Use a significance level of 0.05.