f 56. Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premi- ums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1 ,000. a. Based on this sample information, develop a 90% condence interval for the popula tion mean yearly premium. b. How large a sample is needed to nd the population mean within $250 at 99% condence? @ AGES Century National Bank update on the use of these cards . Develop a 95% confi- Refer to the description of Century National Bank at the dence interval for the proportion of customers using these* end of the Review of Chapters 1 - 4 on page 129 . When Mr. cards . On the basis of the confidence interval , is it reason- Selig took over as president of Century several years ago , able to conclude that more than half of the customers use the use of debit cards was just beginning . He would like an a debit card ? Write a brief report interpreting the results .NO. 78% 2:19 PM 9 viewer.gcu.edu H X 301 Q E 44. An economist uses the price of a gallon of milk as a measure of inflation. She finds that the average price is $3.82 per gallon and the population standard deviation is $0.33. You decide to sample 40 convenience stores, collect their prices for a gallon of milk, and compute the mean price for the sample. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between $3.78 and $3.86? c. What is the probability that the difference between the sample mean and the popu- lation mean is less than $0.01? d. What is the likelihood the sample mean is greater than $3.92? 45. Nike's annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose a sample of 81 customers is surveyed and the population standard devi- ation of sports shoes purchased per year is 2.1. a. What is the standard error of the mean in this experiment? b. What is the probability that the sample mean is between 6 and 7 pairs of sports shoes? c. What is the probability that the difference between the sample mean and the popu- lation mean is less than 0.25 pair? d. What is the likelihood the sample mean is greater than 7 pairs? LYTICS 46. FILE Refer to the North Valley Real Estate data, which report information on the homes sold last year. Assume the 105 homes is a population. Compute the population mean and the standard deviation of price. Select a sample of 10 homes. Compute the mean. Determine the likelihood of a sample mean price this high or higher. 47. FILE Refer to the Baseball 20 16 data, which report information on the 30 Major League Baseball teams for the 20 16 season. Over the last decade, the mean attendance per team followed a normal distribution with a mean of 2.45 million per team and a standard deviation of .71 million. Compute the mean attendance per team for the 2016 season. Determine the likelihood of a sample mean attendance this large or larger from the population. 48. FILE Refer to the Lincolnville School District bus data. Information provided by manufac turers of school buses suggests the mean maintenance cost per year is $4,400 per bus with a standard deviation of $1,000. Compute the mean maintenance cost for the Lin- colnville buses. Does the Lincolnville data seem to be in line with that reported by the manufacturer? Specifically, what is the probability of Lincolnville's mean annual mainte- nance cost, or greater, given the manufacturer's data? C G n 12NO.. 77% 2:22 PM 9 viewer.gcu.edu X E 335 Q 66. Near the time of an election, a cable news service performs an opinion poll of 1,000 prob- able voters. It shows that the Republican contender has an advantage of 52% to 48%) a. Develop a 95% confidence interval for the proportion favoring the Republican candidate. b. Estimate the probability that the Democratic candidate is actually leading. c. Repeat the above analysis based on a sample of 3,000 probable voters. 67. A sample of 352 subscribers to Wired magazine shows the mean time spent using the Internet is 13.4 hours per week, with a sample standard deviation of 6.8 hours. Find the 95% confidence interval for the mean time Wired subscribers spend on the Internet. 68. The Tennessee Tourism Institute (TTI) plans to sample information center visitors entering the state to learn the fraction of visitors who plan to camp in the state. Current estimates are that 35% of visitors are campers. How many visitors would you sample to estimate the population proportion of campers with a 95% confidence level and an allowable error of 2%? Statistical Techniques in Business & Economics, 17th Edition 329 ESTIMATION AND CONFIDENCE INTERVALS 315 NALYTICS 69. FILE Refer to the North Valley Real Estate data, which reports information on homes sold in the area during the last year. Select a random sample of twenty homes. a. Based on your random sample of twenty homes, develop a 95% confidence interval for the mean selling price of the homes. b. Based on your random sample of twenty homes, develop a 95% confidence interval for the mean days on the market. c. Based on your random sample of twenty homes, develop a 95% confidence interval for the proportion of homes with a pool. d. Suppose that North Valley Real Estate employs several agents. Each agent will be randomly assigned twenty homes to sell. The agents are highly motivated to sell homes based on the commissions they earn. They are also concerned about the twenty homes they are assigned to sell. Using the confidence intervals you created, write a general memo informing the agents about the characteristics of the homes they may be assigned to sell. e. What would you do if your confidence intervals did not include the mean of all 105 homes? How could this happen? 70. FILE Refer to the Baseball 2016 data, which report information on the 30 Major League Baseball teams for the 2016 season. Assume the 2016 data represents a sample. C a. Develop a 95% confidence interval for the mean number of home runs per team. b. Develop a 95% confidence interval for the mean batting average by each team. c. Develop a 95% confidence interval for the mean earned run average (ERA) for each team. 71. FILE Refer to the Lincolnville School District bus data. a. Develop a 95% confidence interval for the mean bus maintenance cost. b. Develop a 95% confidence interval for the mean bus odometer miles. c. Write a business memo to the state transportation official to report your results. G V OF CHAPTERS n 12