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

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. store 1 store 52 store 3 88 76 85 84 78 67 88 60 58 82 62 93 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.

Which of the following does not need to be known in order to compute the p-value?

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

An ANOVA procedure is used for data that was obtained from four sample groups each comprised of five observations. The degrees of freedom for the critical value of F are

In order to compare the life expectancies of three different brands of printers, eight printers of each brand were randomly selected. Information regarding the three brands is shown below. Brand A Brand B Brand C Average life in months) 62 52 60 Sample variance 36 25 49 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.

Consider the following results for two samples randomly taken from two populations. Sample A Sample B Sample Size 20 25 Sample Mean 28 22 Sample Standard Deviation 5 6 a. Determine the degrees of freedom for the t distribution. b. At 95% confidence, what is the margin of error? c. Develop a 95% confidence interval for the difference between the two population means.

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80.00 60.00 Sample mean \ 16.75 \ 16.25 Population standard deviation \ 1.00 \ 0.95 -Refer to Exhibit 10-8. The null hypothesis

Consider the following results for two samples randomly taken from two populations. Sample A Sample B Sample Size 28 30 Sample Mean 24 22 Sample Standard Deviation 8 6 a. Determine the degrees of freedom for the t distribution. b. Develop a 95% confidence interval for the difference between the two population means. c. Is there conclusive evidence that one population has a larger mean? Explain.

Consider the following results for two samples randomly taken from two populations. Sample A Sample B Sample Size 25 38 Sample Mean 66 60 Sample Standard Deviation 5 7 a. What are the degrees of freedom for the t distribution? b. At 95% confidence, compute the margin of error. c. Develop a 95% confidence interval for the difference between the two population means.

The following information regarding the ages of full-time and part-time students are given. Using the following data, develop an interval estimate for the difference between the mean ages of the two populations. Use a 5% level of significance. The degrees of freedom for the t distribution is 106. $\bar { x }$ Full-Time Part-Time 27.0 24 s 1.5 2 n 500 60

Exhibit 10-10 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 -Refer to Exhibit 10-10. The mean square between treatments MSTR) equals

Lyon, Inc. manufactures Flash drives on two different manufacturing processes. Because the management of this company is interested in determining if process 1 takes less manufacturing time, they selected independent samples from each process. The results of the samples are shown below. Process 1 Process 2 Sample Size 27 22 Sample Mean in minutes) 10 14 Sample Variance 16 25 a. State the null and alternative hypotheses. b. Determine the degrees of freedom for the t test. c. Compute the test statistic d. At 95% confidence, test to determine if there is sufficient evidence to indicate that process 1 takes a significantly shorter time to manufacture the Flash drives.

The heating bills for a selected sample of houses using various forms of heating are given below. Values are in dollars.) Natural Gas Central Electric Heat Pump 84 95 85 64 60 93 93 89 90 88 96 92 71 90 80 a. At α = 0.05, test to see if there is a significant difference among the average heating bills of the homes. Use the p-value approach. b. Test the above hypotheses using the critical value approach. Let α = .05.

Exhibit 10-9 Two major automobile manufacturers have produced compact cars with the same size engines. We are interested in determining whether or not there is a significant difference in the MPG miles per gallon) of the two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data show the results of the test. Driver Manufacturer A Manufacturer B 1 32 28 2 27 22 3 26 27 4 26 24 5 25 24 6 29 25 7 31 28 8 25 27 -Refer to Exhibit 10-9. At 90% confidence the null hypothesis

Exhibit 10-13 Part of an ANOVA table is shown below. Source of Sum of Degrees Mean Variation Squares of Freedom Square F Between Treatments 64 8 Within Treatments 2 Error Total 100 -Refer to Exhibit 10-13. The number of degrees of freedom corresponding to between treatments is

Exhibit 10-8 In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company A Company B Sample size 80.00 60.00 Sample mean \ 16.75 \ 16.25 Population standard deviation \ 1.00 \ 0.95 -Refer to Exhibit 10-8. The test statistic is

Exhibit 10-10 SSTR = 6,750 H0: μ1=μ2=μ3=μ4 SSE = 8,000 Ha: at least one mean is different nT = 20 -Refer to Exhibit 10-10. The test statistic to test the null hypothesis equals

When an analysis of variance is performed on samples drawn from K populations, the mean square between treatments MSTR) is

For four populations, the population variances are assumed to be equal. Random samples from each population provide the following data. Population Sample Size Sample Mean Sample Variance 1 11 40 23.4 2 11 35 21.6 3 11 39 25.2 4 11 37 24.6 Using a .05 level of significance, test to see if the means for all four populations are the same.

Six observations were selected from each of three populations. The data obtained is shown below. Sample 1 Sample 2 Sample 3 31 37 37 28 32 31 34 34 32 32 24 39 26 32 30 29 33 35 Test at the α = 0.05 level to determine if there is a significant difference in the means of the three populations. Use both the critical value and the p-value approaches.