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

In a completely randomized design involving four treatments, the following information is provided. Treatment 1 Treatment 2 Treatment 3 Treatment 4 Sample Size 50 18 15 17 Sample Mean 32 38 42 48 The overall mean the grand mean) for all treatments is

Recently, a local newspaper reported that part time students are older than full time students. In order to test the validity of its statement, two independent samples of students were selected. Full Time Part Time 26 24 s 2 3 n 42 31 a. Give the hypotheses for the above. b. Determine the degrees of freedom. c. Compute the test statistic. d. At 95% confidence, test to determine whether or not the average age of part time students is significantly more than full time students.

Which of the following is not a required assumption for the analysis of variance?

When the following hypotheses are being tested at a level of significance of α, H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The null hypothesis will be rejected if the p-value is

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. Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 Today Five Years Ago 82.0 88 112.5 54 45.0 36 n -Refer to Exhibit 10-3. The standard error of is

In order to estimate the difference between the average mortgages in the southern and the northern states of the United States, the following information was gathered. South North Sample Size 40 45 Sample Mean in \ 1,000) \ 170 \ 175 Sample Standard Deviation in \ 1,000) \ 5 \ 7 a. Compute the degrees of freedom for the t distribution. b. Develop an interval estimate for the difference between the average of the mortgages in the South and North. Let Alpha = 0.03.

Exhibit 10-2 The following information was obtained from matched samples. The daily production rates for a sample of workers before and after a training program are shown below. Worker Before After 1 20 22 2 25 23 3 27 27 4 23 20 5 22 25 6 20 19 7 17 18 -Refer to Exhibit 10-2. Based on the results of question 18, the

The three major automobile manufacturers have entered their cars in the Indianapolis 500 race. The speeds of the tested cars are given below. Manufacturer A Manufacturer B Manufacturer C 180 177 175 175 180 176 179 167 177 176 172 190 At α = .05, test to see if there is a significant difference in the average speeds of the cars of the auto manufacturers. Use both the critical and p-value approaches.

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is

In an analysis of variance, one estimate of σ2 is based upon the differences between the treatment means and the

Consider the following results for two samples randomly taken from two populations. Sample A Sample B Sample Size 31 35 Sample Mean 106 102 Sample Standard Deviation 8 7 a. Determine the degrees of freedom for the t-distribution. b. Develop a 95% confidence interval for the difference between the two population means.

Exhibit 10-12 Source of Variation Sum of Squares Degrees of Freedom Mean Square F Setween Treatments Within Treatments Error) 180 3 TOTAL 480 18 -Refer to Exhibit 10-12. The mean square between treatments MSTR) is

Exhibit 10-11 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 10-11. The number of degrees of freedom corresponding to within treatments is

The daily production rates for a sample of factory workers before and after a training program are shown below. Let d = After - Before. Worker Before After 1 6 9 2 10 12 3 9 10 4 8 11 5 7 9 We want to determine if the training program was effective. a. Give the hypotheses for this problem. b. Compute the test statistic. c. At 95% confidence, test the hypotheses. That is, did the training program actually increase the production rates?

For a one-tailed test lower tail) at 99.7% confidence, Z =

Consider the following results for two samples randomly taken from two normal populations with equal variances. Sample I Sample II Sample Size 28 35 Sample Mean 48 44 Population Standard Deviation 9 10 a. Develop a 95% confidence interval for the difference between the two population means. b. Is there conclusive evidence that one population has a larger mean? Explain.

Consider the following hypothesis test: μ1 - μ2 ≤ 0 μ1 - μ2 > 0 The following results are for two independent samples taken from two populations. Sample 1 Sample 2 Sample Size 35 37 Sample Mean 43 37 Sample Variance 140 170 a. Determine the degrees of freedom for the t distribution. b. Compute the test statistic. c. Determine the p-value and test the above hypotheses.

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. Procass A Praceas B Sample Size 32 35 Sample Mean in minutes) 43 47 Pupulation Variance ) 64 7 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.

If we are interested in testing whether the mean of population 1 is significantly larger than the mean of population 2, the correct null hypothesis is

Samples were selected from three populations. The data obtained are shown below. Sample 1 Sample 2 Sample 3 10 16 15 13 14 18 12 15 13 Sample Mean 12 15 16.5 Sample Variance 2.0 1.0 4.5 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.