Refer to the Scheer Industries example in Section 8.2. Use 6.83 days as a planning value for the population standard deviation. a. Assuming 95% confidence, what sample size would be required to obtain a margin of error of 0.5 days (round up to the next whole number)? b. Assuming 90% confidence, what sample size would be required to obtain a margin of error of 2 days (round up to the next whole number)? A simple random sample of 60 items resulted in a sample mean of 75. The population standard deviation is 14. a. Compute the 95% confidence interval for the population mean (to 1 decimal). C ) b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). c. What is the effect of a larger sample size on the margin of error? Select For at distribution with 16 degrees of freedom, find the area, or probability, in each region. a. To the right of 2.120. (Use 3 decimals.) 0.025 b. To the left of 1.337. (Use 2 decimals.) 0.10 X c. To the left of -1.746. (Use 2 decimals.) d. To the right of 2.583. (Use 2 decimals.) 0.04 0.01 e. Between -2.120 and 2.120. (Use 2 decimals.) f. Between -1.746 and 1.746. (Use 2 decimals.) 0.95 0.9 eBook The average annual cost of the first year of owning and caring for a large dog is $1,843 (US News and World Report, September 9, 2013). The Irish Red and White Setter Association of America has requested a study to estimate the annual first-year cost for owners of this breed. A sample of 50 will be used. Based on past studies, the population standard deviation is assumed known with = $255. a. What is the margin of error for a 95% confidence interval of the mean cost of the first year of owning and caring for this breed (to 2 decimals)? 70.68 DATA file b. The DATAfile Setters contains data collected from fifty owners of Irish Setters on the cost of the first year of owning and caring for their dogs. Use these data sets to compute the sample mean (to 2 decimals). 70.68 Using this sample, what is the 95% confidence interval for the mean cost of the first year of owning and caring for an Irish Red and White Setter (to 2 decimals)? 1772.32 1913.68 Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long. A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was three minutes. Use that as a planning value for the standard deviation in answering the following questions. a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence. 1.96 b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence. 62 eBook Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its Live Health Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint. 91 34 41 105 84 53 55 74 92 80 52 50 40 46 95 73 73 94 98 80 Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals). 95% confidence interval: $ to $ per visit The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .34. a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (to the nearest whole number)? Use 95% confidence. b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)? c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)? ( )