Exam 13: Experimental Design and Analysis of Variance

In a completely randomized experimental design, 11 experimental units were used for each of the 3 treatments. Part of the ANOVA table is shown below. a.Fill in the blanks in the above ANOVA table. b.At 95% confidence, test to determine whether or not the means of the 3 populations are equal.

Exhibit 13-5 Part of an ANOVA table is shown below. -Refer to Exhibit 13-5. The test statistic is

The final examination grades of random samples of students from three different classes are shown below. At the $\alpha$ = .05 level of significance, is there any difference in the mean grades of the three classes?

The Ahmadi Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below. a.State the null and alternative hypotheses. b.Construct an ANOVA table. c.As the statistical consultant to Ahmadi, what would you advise them? Use a .05 level of significance. Use both the critical and p-value approaches. d.Use Fisher's LSD procedure and determine which population mean (if any) is different from the others. Let $\alpha$ = .05.

Exhibit 13-3 To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. -Refer to Exhibit 13-3. The null hypothesis

In a completely randomized design involving four treatments, the following information is provided. The overall mean (the grand mean) for all treatments is

In order to compare the life expectancies of three different brands of tires, ten tires of each brand were randomly selected and were subjected to standard wear testing procedures. Information regarding the three brands is shown below. Use the above data and test to see if the mean mileage for all three brands of tires is the same. Let $\alpha$ = 0.05. Use both the critical value and p-value approaches.

The mean square is the sum of squares divided by

The ANOVA procedure is a statistical approach for determining whether or not

Part of an ANOVA table involving 8 groups for a study is shown below. a.Complete all the missing values in the above table and fill in the blanks. b.Use $\alpha$ = 0.05 to determine if there is any significant difference among the means of the eight groups.

Exhibit 13-7 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. -Refer to Exhibit 13-7. The mean square between treatments (MSTR) is

Exhibit 13-1 -Refer to Exhibit 13-1. The mean square between treatments (MSTR) equals

In an analysis of variance where the total sample size for the experiment is nT and the number of populations is K, the mean square within treatments is

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. If at 95% confidence we want to determine whether or not the means of the five populations are equal, the p-value is

Random samples of several days' sales of handguns per day in three different states are shown below. We are interested in determining whether or not there is a significant difference in the average sales of guns in the three states a.Compute the overall mean . b.State the null and alternative hypotheses to be tested. c.Show the complete ANOVA table for this test including the test statistic. d.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude? e.Determine the p-value and use it for the test.

Exhibit 13-4 In a completely randomized experimental design involving five treatments, 13 observations were recorded for each of the five treatments (a total of 65 observations). The following information is provided. SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The sum of squares within treatments (SSE) is

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes (in $1,000). At $\alpha$ = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments. Use both the critical and p-value approaches.

Employees of MNM Corporation are about to undergo a retraining program. Management is trying to determine which of three programs is the best. They believe that the effectiveness of the programs may be influenced by sex. A factorial experiment was designed. You are given the following information. a.Set up the ANOVA table. b.What advice would you give MNM? Use a .05 level of significance.

Exhibit 13-6 Part of an ANOVA table is shown below. -Refer to Exhibit 13-6. The number of degrees of freedom corresponding to between treatments is

At $\alpha$ = 0.05, test to determine if the means of the three populations (from which the following samples are selected) are equal. Use both the critical and p-value approaches.