17. Customers at Costco spend an average of $130 per trip ( The Wall Street Journal , October 6, 2010). One of Costco's rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population standard deviation is $10.50 and that spending follows a normal distribution. a. Specify the appropriate null and the alternative hypotheses to test whether average spending at the rival's store is more than $130. Test Statistic = 2.500 H0: = 130 Sample mean = 135.25 Ha: > 130 Standard deviation = 10.5 Standard error of mean = / n b. Calculate the value of the test statistic. Calculate the p-value. Standard error of mean = 10.5 / 25 Test Statistic = 2.500 SE = 10.5/5 P-Value = 0.0062 Standard error of mean 2.1 c. At the 5% significance level, what is the conclusion? z = (xbar- ) / SE z = (135.25-130) / 2.1 Since 5%is higher than the p-value of .0062 z = 2.5 then the hypothese null gets rejected. P-value = P( z > 2.5) = 0.0062 If alpha = 0.05, the critical value is 1.645 d. Repeat the test using the critical value approach. 1.645 Since the 2.5 test statistic is higher than the critical value of 1.645 then the hypothese null gets rejected. 23. Use the hourly wage data. An economist wants to test if the average hourly wage is less than $22. Hourly Wage 37.85 21.72 14.34 21.26 24.65 25.65 15.45 20.39 29.13 27.33 18.02 20.39 24.18 17.29 15.61 35.07 40.33 20.39 16.61 16.33 23.15 20.39 14.88 13.88 17.65 15.45 26.35 19.15 16.61 18.39 15.45 18.02 13.44 17.66 16.96 14.34 15.45 17.43 35.89 20.39 11.81 15.45 17.66 13.87 16.35 15.45 23.67 16.02 23.15 24.18 a. State the null and the alternative hypotheses for the test. H0: 22 HA: < 22 b. Use the function Z.TEST to calculate the p-value. Assume that the population standard deviation is $6. 0.98252 c. At = 0.05 what is the conclusion? Is the average hourly wage less than $22? 36. The manager of a small convenience store does not want her customers standing in line for too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than five minutes. She randomly observes the wait time (in minutes) of customers during the day as: 3.5 5.8 7.2 1.9 6.8 8.1 5.4 a. Set up the null and the alternative hypotheses to determine if the manager needs to hire another employee. H0: 5 < HA: > 5 b. Calculate the value of the test statistic. What assumption regarding the population is necessary to implement this step? c. Use the critical value approach to decide whether the manager needs to hire another employee at = 0.10 . sample size sample size average 7 5.528571 d. Repeat the above analysis with the p -value approach