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

The Ahmadi Corporation wants to increase the productivity of its line workers. Four different programs have been suggested to help increase productivity. Twenty employees, making up a sample, have been randomly assigned to one of the four programs and their output for a day's work has been recorded. You are given the results below. Propram A Propram B Propram C Propram D 150 150 185 175 130 120 220 150 120 135 190 120 180 160 180 130 145 110 175 175 a. State the null and alternative hypotheses. b. Construct an ANOVA table. c. As the statistical consultant to Ahmadi, what would you advise them? Use a .05 level of significance. Use both the critical and p-value approaches.

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 within treatments MSE) equals

For a one-tailed test lower tail) at 93.7% confidence, Z =

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 point estimate for the difference between the means of the two populations 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. If at 95% confidence, we want to determine whether or not the means of the populations are equal, the p-value is

A recent Time magazine reported the following information about a sample of workers in Germany and the United States. United States Germany Average length of workweek hours) 42 38 Sample Standard Deviation 5 6 Sample Size 600 700 We want to determine whether or not there is a significant difference between the average workweek in the United States and the average workweek in Germany. a. State the null and the alternative hypotheses. b. Compute the test statistic. c. Compute the p-value. What is your conclusion?

A test on world history was given to a group of individuals before and also after a film on the history of the world was presented. The results are given below. We want to determine if the film significantly increased the test scores. For the following matched samples, let the difference "d" be d = after - before.) Individual After Befor 1 92 86 2 86 88 3 89 84 4 90 90 5 93 85 6 88 90 7 97 91 a. Give the hypotheses for this problem. b. Compute the test statistic. c. At 95% confidence, test the hypotheses.

A credit company has gathered information regarding the average amount owed by people under 30 years old and by people over 30 years. Independent random samples were taken from both age groups. You are given the following information. Under 30 Over 30 600 550 n 200 300 361 400 Construct a 95% confidence interval for the difference between the average amounts owed by the two age groups.

The critical F value with 6 numerator and 60 denominator degrees of freedom at α = .05 is

To compute an interval estimate for the difference between the means of two populations, the t distribution

Exhibit 10-6 The management of a department store is interested in estimating the difference between the mean credit purchases of customers using the store's credit card versus those customers using a national major credit card. You are given the following information. Store's Card Major Credit Card Sample size 64 49 Sample mean \ 140 \ 125 Population standard deviation \ 10 \ 8 -Refer to Exhibit 10-6. A 95% confidence interval estimate for the difference between the average purchases of the customers using the two different credit cards is

The business manager of a local health clinic is interested in estimating the difference between the fees for extended office visits in her center and the fees of a newly opened group practice. She gathered the following information regarding the two offices. Health Clinic Group Practice Sample size 50 visits 45 visits Sample mean \ 21.00 \ 19.00 Standard deviation \sigma) \ 2.75 \ 3.00 Develop a 95% confidence interval estimate for the difference between the average fees of the two offices.

The following information regarding the yearly salaries in $1,000) of CEO's in 2010 and 2009 are provided. Year 2010 Year 2009 Sample size 190 145 Sample Mean 560 540 Population Standard Deviation 80 90 a. At 95% confidence, perform a test to determine if there has been a significant increase in the salaries of CEO's. Use the Critical Value Approach. b. Compute the p-value.

Allied Corporation is trying to determine whether to purchase Machine A or B. It has leased the two machines for a month. A random sample of 5 employees has been taken. These employees have gone through a training session on both machines. Below you are given information on their productivity rate on both machines. Let the difference d = Machine A - Machine B.) Productivity Rate Parson Machine A Machin B 1 47 52 2 53 58 3 50 47 4 55 60 5 45 53 a. State the null and alternative hypotheses for a two-tailed test. b. Find the mean and standard deviation for the difference. c. Compute the test statistic. d. Test the null hypothesis stated in Part a at the 10% level.