Exam 10: Comparisons Involving Means, Experimental Design and Analysis of Variance

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. Note that the sample sizes are not equal. a.Compute the overall mean. b.At $\alpha$ = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. Use both the critical value and p-value approaches.

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

The heating bills for a selected sample of houses using various forms of heating are given below (values are in dollars). At $\alpha$ = 0.05, test to see if there is a significant difference among the average bills of the homes. Use both the critical and p-value approaches.

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

Exhibit 10-3 A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. -Refer to Exhibit 10-3. What is the conclusion that can be reached about the difference in the average final examination scores between the two classes? (Use a .05 level of significance.)

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 $\alpha$ = 0.05 to determine if there is a significant difference in the mean hourly units of production for the three types of production processes. Use both the critical and p-value approaches.

Maxforce, Inc., manufactures racquetball racquets by two different manufacturing processes (A and B). Because the management of this company is interested in estimating the difference between the average time it takes each process to produce a racquet, they select independent samples from each process. The results of the samples are shown below. a.Develop a 95% confidence interval estimate for the difference between the average time of the two processes. b.Is there conclusive evidence to prove that one process takes longer than the other? If yes, which process? Explain.

Random samples of individuals from three different cities were asked how much time they spend per day watching television. The results (in minutes) for the three groups are shown below. At $\alpha$ = 0.05, test to see if there is a significant difference in the averages of the three groups.

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.

Two independent random samples of annual starting salaries for individuals with masters and bachelors degrees in business were taken and the results are shown below a.What are the degrees of freedom for the t distribution? b.Provide a 95% confidence interval estimate for the difference between the salaries of the two groups.

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?

Exhibit 10-12 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. -Refer to Exhibit 10-12. The sum of squares within treatments (SSE) is

Exhibit 10-10 -Refer to Exhibit 10-10. The test statistic to test the null hypothesis equals

Exhibit 10-12 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. -Refer to Exhibit 10-12. The mean square within treatments (MSE) is

If we are interested in testing whether the mean of items in population 1 is larger than the mean of items in population 2, the

We are interested in testing the following hypotheses. H₀: $\mu$ ₁- $\mu$ ₂ $\ge$ 0 H_a: $\mu$ ₁- $\mu$ ₂ < 0 The test statistic Z is computed to be 2.83. The p-value for this test is

Exhibit 10-13 Part of an ANOVA table is shown below. -Refer to Exhibit 10-13. The mean square within treatments (MSE) is

In a completely randomized experimental design, 18 experimental units were used for the first treatment, 10 experimental units for the second treatment, and 15 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, test to see if there is a significant difference among the means.

In the analysis of variance procedure (ANOVA), "factor" refers to

Exhibit 10-5 The following information was obtained from matched samples. -Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis