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

In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken and the following information is collected. Modal A Modal B Sample Size 60 55 Sample Mean 28 25 Smple Variance 16 9 a. At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. b. Is there conclusive evidence to indicate that one model gets a higher MPG than the other? Why or why not? Explain.

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 within treatments 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 null hypothesis is to be tested at the 5% level of significance. The p-value is

Random samples of several days' sales of handguns per day in three different states are shown below. We are interested in determining whether or not there is a significant difference in the average sales of guns in the three states T ennessee Kentucky Texas 12 15 16 13 19 18 17 20 10 18 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.

The management of Chattanooga Paper Corporation wants to determine whether there is a significant difference in the thickness of papers produced at their two existing plants. The following data has been accumulated for this test The degrees of freedom df) for this problem are df = 51. Plant 1 Plant 2 Sample Mean 23.6 23.1 Sample Variance ) 25 4 Sample Size 42 53 a. Compute a 95% confidence interval for the difference in the average thickness of papers produced at the two plants. Please use the same order as given above. b. Is there conclusive evidence that the average thickness in one plant is significantly more than the other? If yes, which plant? Explain, using the results of part a). Do not perform any tests.

Exhibit 10-4 The following information was obtained from independent random samples. Assume normally distributed populations with equal variances. Sample 1 Sample 2 Sample Mean 45 42 Sanple Variance 85 90 Sample Size 10 12 -Refer to Exhibit 10-4. The standard error of is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary in \ 1,000) 44 41 Population Variance ) 128 72 -Refer to Exhibit 10-1. At 95% confidence, the margin of error is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary in \ 1,000) 44 41 Population Variance ) 128 72 -Refer to Exhibit 10-1. If you are interested in testing whether or not the average salary of males is significantly greater than that of females, the test statistic is

Exhibit 10-1 Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary in \ 1,000) 44 41 Population Variance ) 128 72 -Refer to Exhibit 10-1. The p-value is

Random samples of employees from three different departments of MNM Corporation showed the following yearly incomes in $1,000). Department A Department B Department C 40 46 46 37 41 40 43 43 41 41 33 48 35 41 39 38 42 44 At α = .05, test to determine if there is a significant difference among the average incomes of the employees from the three departments. Use both the critical and p-value approaches.

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. A point estimate for the difference between the two sample means is

The critical F value with 8 numerator and 29 denominator degrees of freedom at α = 0.01 is

The final examination grades of random samples of students from three different classes are shown below. Class A Class B Class C 92 91 85 85 85 93 96 90 82 95 86 84 At the α = .05 level of significance, is there any difference in the mean grades of the three classes?

Guitars R. US has three stores located in three different areas. Random samples of the sales of the three stores in $1000) are shown below. Store 1 Store 2 Store 3 80 85 79 75 86 85 76 81 88 89 80 80 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.

Samples of employees of Companies A and B provided the following information regarding the ages of employees. Company A Company B Sample Size 32 36 Average Age 42 47 variance 16 36 Develop a 97% confidence interval for the difference between the average ages of the employees of the two companies.

Random samples were selected from three populations. The data obtained are shown below. Please note that the sample sizes are not equal. Treatment 1 Treatment 2 Treatment 3 37 43 28 33 39 32 36 35 33 38 38 40 a. Compute the overall mean . b. At 95% confidence using the critical value and p-value approach, test to see if there is a significant difference among the means.

The management of Chattanooga Paper Corporation wants to determine whether there is a significant difference in the thickness of papers produced at their two existing plants. The following data has been accumulated for this test. The degrees of freedom df) for this problem are given to be df = 80. Plant 1 Plant 2 Sample Mean 30.8 30.0 Sample Standard Deviation 8.0 9.0 Sample Size 55 41 a. Compute a 95% confidence interval for the difference in the average thickness of papers produced at the two plants. b. Is there conclusive evidence that the average thickness in one plant is significantly more than the other? If yes, which plant? Explain, using the results of part a). Do not perform any test.

Exhibit 10-5 The following information was obtained from matched samples. Individual Method 1 Method 2 1 7 5 2 5 9 3 6 8 4 7 7 5 5 6 -Refer to Exhibit 10-5. If the null hypothesis is tested at the 5% level, the null hypothesis

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. If at 95% confidence we want to determine whether or not the means of the five populations are equal, the p-value is

Exhibit 10-14 The following is part of an ANOVA table that was obtained from data regarding three treatments and a total of 15 observations. Source of Variation Sum of Squares Degrees of Freedom Between Treatments 64 Error Within Treatments) 96 -Refer to Exhibit 10-14. The number of degrees of freedom corresponding to within treatments is