Chapter%203%20-%20Extra%20Practice%20Problems

# Chapter%203%20-%20Extra%20Practice%20Problems - Econ 120B...

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Econ 120B Chapter 3 – Extra Practice Problems 1. A mail order business prides itself in its ability to fill customers’ orders in six days, in average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based upon this sample information, he decides whether the desired standard is being met. He will assume that the average number of days to fill the customers’ orders is six or less unless the data suggest strongly otherwise. a. Establish the appropriate null and alternative hypotheses. b. On one occasion where a sample of 40 customers was selected, the average number of days was 6.65, with a sample standard deviation of 1.5 days. Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.05 to answer this question. c. Calculate the p-value for this test. Conduct the test using this p-value. d. The operation manager wishes to monitor the efficiency of his mail-order service often. Therefore, he does not wish to repeatedly calculate t-values to conduct hypothesis tests. Obtain the critical value for the average number of days, so that the manager can simply compare the sample mean to this value to conduct the test. Use the specific sample average of 6.65 to conduct the test. 2. The director of a state agency believes that the average starting salary for clerical employees in the state is less than \$30,000 per year. To test her hypothesis she has collected a simple random sample of 100 starting clerical salaries from across the state and found that the sample means is \$29,750. a. State the appropriate null and alternative hypotheses. b. Assuming the population standard deviation is known to be \$2,500 and the significance level for the test is to be 0.05, what is the critical value (stated in dollars)?. c. Referring to your answer in part b., what conclusion should be reached with respect to the null hypothesis? d. Referring to your answer in part c., which of the two statistical errors might have been made in this case? Explain. 3. The manager of a fitness club in San Diego believes that the recent remodeling project has greatly improved the club’s appeal for members and they now stay longer at the club per visit than before remodeling. Studies show that the previous mean time per visit was 36 minutes, with a standard deviation of 11 minutes. A simple random sample of n = 200 visits is selected, and the current sample

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Chapter%203%20-%20Extra%20Practice%20Problems - Econ 120B...

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