42. U.S. News & World Report publishes comprehensive information on America's best colleges (America's Best Colleges, 2009 ed.). Among other things, they provide a listing of their 133 best national universities. You would like to take a sample of these universities for a follow-up study on their students. Begin at the bottom of the third column of random digits in Table 7.1. Ignoring the first two digits in each five-number group and using the three-digit random numbers beginning with 959 read up the column to identify the number (from 1 to 133) of the first seven universities to be included in a simple random sample. Continue by starting at the bottom of the fourth and fifth columns and reading up if necessary. 44. Foot Locker uses sales per square foot as a measure of store productivity. Sales de currently running at an annual rate of $406 per square foot (The Wall Street Journal, March 7, 2012). You have been asked by management to conduct a study of a sample of 64 Foot Locker stores. Assume the standard deviation in annual sales per square foot for the population of all 3400 Foot Locker stores is $80. a. Show the sampling distribution of X, the sample mean annual sales per square foot for a sample of 64 Foot Locker stores. b. What is the probability that the sample mean will be within S15 of the population mean? c. Suppose you find a sample mean of $380. What is the probability of finding a sample mean of $380 or less? Would you consider such a sample to be an unusually low performing group of stores? a. 46. After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27.175 (U.S. News & World Report, America's Best Colleges. 2009 ed.). Assume the population standard deviation is $7,400. Suppose that a random sample of 60 USC students will be taken from this population. What is the value of the standard error of the mean? b. What is the probability that the sample mean will be more than $27.175? What is the probability that the sample mean will be within $1,000 of the population mean? d. How would the probability in part (e) change if the sample size were increased to 1002 c. 48 A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500. How large was the sample used in this survey? b. What is the probability that the point estimate was within 25 of the population mean? 50. Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website, October 23, 2012). Answer the following questions based on a sample of 240 Australians Show the sampling distribution of p, the sample proportion of Australians who are smokers. b. What is the probability the sample proportion will be within 1.04 of the population proportion? What is the probability the sample proportion will be within 1.02 of the population proportion? a. C. 52. Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraudthe practice of someone clicking on an ad solely for the purpose of driving up advertising revenue has become a problem. Forty percent of ad- vertisers claim they have been a victim of click fraud (Business Week, March 13, 2006). Suppose a simple random sample of 380 advertisers will be taken to learn more about how they are affected by this practice. a. What is the probability that the sample proportion will be within 1.04 of the population proportion experiencing click fraud? b. What is the probability that the sample proportion will be greater than .45? 54. Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields a standard error of the proportion of .0625. a. How large was the sample used in this analysis? That is, how many sales calls did Lori make during the month? b. Let p indicate the sample proportion of book adoptions obtained during the month. Show the sampling distribution of p. c. Using the sampling distribution of p. compute the probability that Lori will obtain book adoptions on 30% or more of her sales calls during a one-month period. 42. U.S. News & World Report publishes comprehensive information on America's best colleges (America's Best Colleges, 2009 ed.). Among other things, they provide a listing of their 133 best national universities. You would like to take a sample of these universities for a follow-up study on their students. Begin at the bottom of the third column of random digits in Table 7.1. Ignoring the first two digits in each five-number group and using the three-digit random numbers beginning with 959 read up the column to identify the number (from 1 to 133) of the first seven universities to be included in a simple random sample. Continue by starting at the bottom of the fourth and fifth columns and reading up if necessary. 44. Foot Locker uses sales per square foot as a measure of store productivity. Sales de currently running at an annual rate of $406 per square foot (The Wall Street Journal, March 7, 2012). You have been asked by management to conduct a study of a sample of 64 Foot Locker stores. Assume the standard deviation in annual sales per square foot for the population of all 3400 Foot Locker stores is $80. a. Show the sampling distribution of X, the sample mean annual sales per square foot for a sample of 64 Foot Locker stores. b. What is the probability that the sample mean will be within S15 of the population mean? c. Suppose you find a sample mean of $380. What is the probability of finding a sample mean of $380 or less? Would you consider such a sample to be an unusually low performing group of stores? a. 46. After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27.175 (U.S. News & World Report, America's Best Colleges. 2009 ed.). Assume the population standard deviation is $7,400. Suppose that a random sample of 60 USC students will be taken from this population. What is the value of the standard error of the mean? b. What is the probability that the sample mean will be more than $27.175? What is the probability that the sample mean will be within $1,000 of the population mean? d. How would the probability in part (e) change if the sample size were increased to 1002 c. 48 A researcher reports survey results by stating that the standard error of the mean is 20. The population standard deviation is 500. How large was the sample used in this survey? b. What is the probability that the point estimate was within 25 of the population mean? 50. Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website, October 23, 2012). Answer the following questions based on a sample of 240 Australians Show the sampling distribution of p, the sample proportion of Australians who are smokers. b. What is the probability the sample proportion will be within 1.04 of the population proportion? What is the probability the sample proportion will be within 1.02 of the population proportion? a. C. 52. Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraudthe practice of someone clicking on an ad solely for the purpose of driving up advertising revenue has become a problem. Forty percent of ad- vertisers claim they have been a victim of click fraud (Business Week, March 13, 2006). Suppose a simple random sample of 380 advertisers will be taken to learn more about how they are affected by this practice. a. What is the probability that the sample proportion will be within 1.04 of the population proportion experiencing click fraud? b. What is the probability that the sample proportion will be greater than .45? 54. Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that a statistical analysis of the data yields a standard error of the proportion of .0625. a. How large was the sample used in this analysis? That is, how many sales calls did Lori make during the month? b. Let p indicate the sample proportion of book adoptions obtained during the month. Show the sampling distribution of p. c. Using the sampling distribution of p. compute the probability that Lori will obtain book adoptions on 30% or more of her sales calls during a one-month period