Exam 13: Experimental Design and Analysis of Variance

Samples were selected from three populations. The data obtained are shown below. a.Compute the overall mean . b.Set up an ANOVA table for this problem. c.At 95% confidence, test to determine whether there is a significant difference in the means of the three populations. Use both the critical and p-value approaches.

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

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

A dietician wants to see if there is any difference in the effectiveness of three diets. Eighteen people were randomly chosen for the test. Then each individual was randomly assigned to one of the three diets. Below you are given the total amount of weight lost in six months by each person. a.State the null and alternative hypotheses. b.Calculate the test statistic. c.What would you advise the dietician about the effectiveness of the three diets? Use a .05 level of significance.

In a completely randomized experimental design, 11 experimental units were used for each of the 4 treatments. Part of the ANOVA table is shown below. Fill in the blanks in the above ANOVA table.

Carolina, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (in $1,000) are shown below. Please note that the sample sizes are not equal. a.Compute the overall mean . b.At 95% confidence, test to see if there is a significant difference in the average sales of the three stores. Use both the critical value and p-value approaches. Show your complete work and the ANOVA table.

Exhibit 13-2 -Refer to Exhibit 13-2. The mean square between treatments equals

Three universities in your state decided to administer the same comprehensive examination to the recipients of MBA degrees from the three institutions. From each institution, MBA recipients were randomly selected and were given the test. 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.) Use both the critical and p-value approaches.

Nancy, Inc. has three stores located in three different areas. Random samples of the sales of the three stores (In $1,000) are shown below. a.Compute the overall mean . b.At 95% confidence, test to see if there is a significant difference in the average sales of the three stores.

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 computed test statistics is

In a completely randomized experimental design, 7 experimental units were used for the first treatment, 9 experimental units for the second treatment, and 14 experimental units for the third treatment. Part of the ANOVA table for this experiment is shown below. a.Fill in all the blanks in the above ANOVA table. b.At 95% confidence using both the critical value and p-value approaches, test to see if there is a significant difference among the means.

MNM, Inc. has three stores located in three different areas. Random samples of the daily sales of the three stores (in $1,000) are shown below. At 95% confidence, test to see if there is a significant difference in the average sales of the three stores. Use both the critical and p-value approaches.

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 mean square between treatments (MSTR) is

Exhibit 13-1 -Refer to Exhibit 13-1. The test statistic to test the null hypothesis equals

In a completely randomized experimental design, 14 experimental units were used for each of the 5 levels of the factor (i.e., 5 treatments). Fill in the blanks in the following ANOVA table.

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 between treatments (MSTR) equals

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

The number of times each experimental condition is observed in a factorial design is known as

A term that means the same as the term "variable" in an ANOVA procedure is

In the ANOVA, treatment refers to