# SOLUTION: 1. The null and alternate hypotheses are: Ho: U1= U2 H1: U1=/ U2 - The /should be place across the equal sign A random sample of 15 observations from the first population r

Algebra ->  Algebra  -> Probability-and-statistics -> SOLUTION: 1. The null and alternate hypotheses are: Ho: U1= U2 H1: U1=/ U2 - The /should be place across the equal sign A random sample of 15 observations from the first population r      Log On

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 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Probability-and-statistics Question 62589: 1. The null and alternate hypotheses are: Ho: U1= U2 H1: U1=/ U2 - The /should be place across the equal sign A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means? Use the five-step hypothesis testing procedure for the following exercises 2. Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information Sales (\$) 131 135 146 165 136 142 Audit (\$) 130 102 129 143 149 120 139 At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value? 3. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded Salesperson Before After Salesperson Before After Sid Mahone Before \$320 After \$340 Carol Quick Before 290 After 285 Tom Jackson Before 421 After 475 Jack Walker Before 402 After 500 Peg Mancuso Before 625 After 631 Anita Loma Before 560 After 560 John Cuso Before 360 After 365 Carl Utz Before 431 After 431 A. S. Kushner Before 506 After 525 Fern Lawton Before 505 After 619 4. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger? Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!Ho: U1= U2 H1: U1=/ U2 - The /should be place across the equal sign A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, is there a difference in the population means? Use the five-step hypothesis testing procedure for the following exercises -------- x1-bar=350 x2-bar=342 Standard Dev. = sqrt[(s1^2/n1)+(s2^2/n2) =sqrt[(12)^2/15+(15)^2/17]=4.77 Test Statistic: t(350-342)=8/4.77=1.67 Critical Value for alpha = 0.10: 1.695 ------- Since Test Statistic is > critical value, Fail to reject the null hypothesis. --------- If you do this with p-values you find p=0.1045... if you don't pool and p=0.1092... if you do pool. In either case since p>alpha you fail to reject Ho --------------- 2. Ms. Lisa Monnin is the budget director for Nexus Media, Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information Sales (\$) 131 135 146 165 136 142 Audit (\$) 130 102 129 143 149 120 139 At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is the p-value? p=0.076 if data is pooled p=0.073 if data is not pooled -------- In either case p<0.10 so Reject the Ho that the means are equal There is sufficient statistical evidence to support the claim that the travel expenses for the sales staff are greater than the travel expenses of the admin stall. ------------------ 3. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded Salesperson Before After Salesperson Before After Sid Mahone Before \$320 After \$340 Carol Quick Before 290 After 285 Tom Jackson Before 421 After 475 Jack Walker Before 402 After 500 Peg Mancuso Before 625 After 631 Anita Loma Before 560 After 560 John Cuso Before 360 After 365 Carl Utz Before 431 After 431 A. S. Kushner Before 506 After 525 Fern Lawton Before 505 After 619 --------What is the question??? -------------- 4. Clark Heter is an industrial engineer at Lyons Products. He would like to determine whether there are more units produced on the afternoon shift than on the day shift. A sample of 54 day-shift workers showed that the mean number of units produced was 345, with a standard deviation of 21. A sample of 60 afternoon-shift workers showed that the mean number of units produced was 351, with a standard deviation of 28 units. At the .05 significance level, is the number of units produced on the afternoon shift larger? If not pooled, p=0.902 If pooled , p=0.898... In either case p>5% so Fail to reject Ho. There is not sufficient statistical evidence to conclude the afternoon shift produces more units than the day shift. -------- Cheers, Stan H.