Name(s) ECON 2370: Introduction to Economic Data Analysis Due date: Monday, March 21 (Mo-We section) Tuesday, March 22 (Tu-Th sections) PS# Class time: Spring 2016 Homework # 5 1. The mean preparation fee H&R Block charged retail customers last year was $183 (The Wall Street Journal, March 7, 2012). Use this price as the population mean and assume the population standard deviation of preparation fees is $50. a. What is the probability that the mean price for a sample of 30 H&R Block retail customers is within $8 of the population mean (i.e. +/- $8)? b. What is the probability that the mean price for a sample of 50 H&R Block retail customers is within $8 of the population mean? 2. People end up tossing 12% of what they buy at the grocery store (Reader's Digest, March 2009). Assume this is the true population proportion and that you plan to take a sample survey of 540 grocery shoppers to further investigate their behavior. p a. Show the sampling distribution of , the proportion of groceries thrown out by your sample respondents. b. What is the probability that your survey will provide a sample proportion within +/0.03 of the population proportion? c. What is the probability that your survey will provide a sample proportion within +/0.015 of the population proportion? 1 3. The Wall Street Journal reported that automobile crashes cost the United States $162 billion annually (The Wall Street Journal, March 5, 2008). The average cost per person for crashes in the Tampa, Florida, area was reported to be $1599. Suppose this average cost was based on a sample of 50 persons who had been involved in car crashes and that the population standard deviation is = $600. a. What is the 95% confidence interval for the population mean? b. Write the interpretation of your answer in words. c. Determine the appropriate sample size for a margin of error of $100 with a 99% confidence level? 4. The average cost per night of a hotel room in New York City is $273 (SmartMoney, March 2009). Assume this estimate is based on a sample of 45 hotels and that the sample standard deviation is $65. a. What is the 95% confidence interval estimate of the population mean? b. Two years ago the average cost of a hotel room in New York City was $229. Discuss the change in cost over the two-year period. 5. The percentage of people not covered by health care insurance in 2003 was 15.6% (Statistical Abstract of the United States, 2006). A congressional committee has been charged with conducting a sample survey to obtain more current information. 2 a. What is the 95% confidence interval for the population proportion? b. Repeat part (a) using a 99% confidence level. c. What is the appropriate sample size to estimate a 90% confidence interval with a margin of error of +/-0.03? 3