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Study Questions on Ch.11 1) An induatrial engineer at the Lyons Products would like to determine whether there are more units produced on the night shift than on the day shift. Assume the population standard deviation for the number of units produced on the day shift is 21 and is 28 on the night shift. A sample of 54 day-shift workers showed that the mean number of units produced on the day shift was 345. A sample of 60 nightshift workers showed that the mean number of units produced on the day shift was 351. At the 0.05 significance level, is the number of units produced on the night shift larger? Answer: Step 1: Ho: 1 2 H1: 1 < 2 Step 2: 0.05 Step 4: z (Note: 1 represents day shift and 2 represents night shift) Step 3 : Reject Ho if z < 1.65 345 351 (21) 2 (28) 2 54 60 1.30 Step 5: Fail to reject Ho. There is not enough evidence to conclude that more units are produced on the afternoon shift. 2) Each month the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: Do you think the economy is contracting? Last month, out of 300 responders 160 answered “yes” to the question. This month 170 of the 290 said the economy was contracting. At the 0.05 significance level can we conclude that a larger proportion of the agents believe the economy is contracting this month? Answer: Step 1: Ho: 1 2 H1: 1 < 2 Step 2: 0.05 (Note: 1 is for last month and 2 is for this month) Step 3: If z < 1.65, reject Ho. Step 4: pc 160 170 0.56 300 290 z 0.5333 0.5862 1.29 (0.56)(0.44) (0.56)(0.44) 300 290 Step 5: Do not reject the null. We cannot conclude an increased proportion believe the economy is contracting. 3) The owner of King Burger wants to compare the sales per day at two locations. The mean number sold for 10 randomly selected days at Kyrenia branch was 83.55 and the sample standard deviation was 10.50. For a random sample of 12 days at Famagusta branch, the mean number sold was 78.80 and the standard deviation was 14.25. At the 0.05 significance level, is there a difference in the mean number of hamburgers sold at the two branches? Answer: Step 1: Ho: n = s H1: n s Step 3: df n1 n2 2 10 12 2 20 critical t value: 2.086. So, reject null hypothesis if if computed t is less than -2.086 or if greater than 2.086 Step 2: 0.05 Step 4: 2 2 (10 1)(10.5) 2 (12 1)(14.25) 2 2 ( n1 1) s1 ( n2 1) s 2 sp 161.3 n1 n2 2 20 t X1 X 2 83.55 78.8 4.75 0.873 5.438 1 1 1 1 ) 161.3 n1 n2 10 12 Step 5: Cannot reject null hypothesis and conclude there is no evidence that sales at two locations are different. s 2p (