Exam 13: Experimental Design and Analysis of Variance

Individuals were randomly assigned to three different production processes. The hourly units of production for the three processes are shown below. Use the analysis of variance procedure with $\mu$ = 0.05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes.

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -Refer to Exhibit 13-7. If at a 5% level of significance, we want to determine whether or not the means of the populations are equal, the critical value of F is

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university. At $\alpha$ = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. (Note that the sample sizes are not equal.)

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -Six observations were selected from each of three populations. The data obtained is shown below: Test at $\alpha$ = 0.05 level to determine if there is a significant difference in the means of the three populations.

Exhibit 13-2 -Refer to Exhibit 13-2. The sum of squares due to error equals

An ANOVA procedure is applied to data obtained from 6 samples where each sample contains 20 observations. The degrees of freedom for the critical value of F are

Samples were selected from three populations. The data obtained are shown below. At a 5% level of significance, use Excel to test to determine whether there is a significant difference in the means of the three populations.

Allied 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 Allied, what would you advise them? Use a .05 level of significance. d.Use Fisher's LSD procedure and determine which population mean (if any) is different from the others. Let $\alpha$ = .05.

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 $\mu$ = 0.01 to determine if there is any significant difference among the means of the eight groups.

Exhibit 13-2 -Refer to Exhibit 13-2. The null hypothesis for this ANOVA problem is

Three different models of automobiles (A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below. Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let Alpha = 0.05.

Exhibit 13-4 In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. The mean square between treatments (MSTR) is

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -In an analysis of variance, one estimate of ² is based upon the differences between the treatment means and the

A factorial experiment involving 2 levels of factor A and 2 levels of factor B resulted in the following. Use Excel and test for any significant main effect and any interaction effect. Use $\alpha$ = .05.

Exhibit 13-5 Part of an ANOVA table is shown below. -Refer to Exhibit 13-5. The conclusion of the test is that the means

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 gender. 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 13-3 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 mean square within treatments (MSE) equals

Exhibit 13-1 -Refer to Exhibit 13-1. The mean square within treatments (MSE) equals

Exhibit 13-4 In a completely randomized experimental design involving five treatments, thirteen observations were recorded for each of the five treatments. The following information is provided.SSTR = 200 (Sum Square Between Treatments) SST = 800 (Total Sum Square) -Refer to Exhibit 13-4. If at a 5% level of significance we want to determine whether or not the means of the five populations are equal, the critical value of F is

Exhibit 13-7 The following is part of an ANOVA table, which was the results of three treatments and a total of 15 observations. -Information regarding the ACT scores of samples of students in four different majors are given below. a.Set up the ANOVA table for this problem. b.At a 5% level of significance, test to determine whether there is a significant difference in the means of the four populations.