306 CHAPTER 6 Confidence Intervals In Exercises 25–28, use the confidence interval to find the margin of error and the sample mean. 25. (12.0, 14.8) 26. (21.61, 30.15) 27. (1.71, 2.05) 28. (3.144, 3.176) In Exercises 29–32, determine the minimum sample size n needed to estimate m for the values of c, s, and E. 29. c = 0.90, s = 6.8, E = 1 30. c = 0.95, s = 2.5, E = 1 31. c = 0.80, s = 4.1, E = 2 32. c = 0.98, s = 10.1, E = 2 Using and Interpreting Concepts Finding the Margin of Error In Exercises 33 and 34, use the confidence interval to find the estimated margin of error. Then find the sample mean. 33. Commute Times A government agency reports a confidence interval of (26.2, 30.1) when estimating the mean commute time (in minutes) for the population of workers in a city. 34. Book Prices A store manager reports a confidence interval of (244.07, 280.97) when estimating the mean price (in dollars) for the population of textbooks. Constructing Confidence Intervals In Exercises 35–38, you are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. 35. Gold Prices From a random sample of 48 business days from May 9, 2016, through May 7, 2021, U.S. gold prices had a mean of $1404.09. Assume the population standard deviation is $232.09. (Source: Federal Reserve Bank of St. Louis) 36. Stock Prices From a random sample of 36 business days during the year 2020, the mean closing price of Apple stock was $97.17. Assume the population standard deviation is $21.77. (Source: Nasdaq) 37. Video Game Prices From a random sample of 50 Nintendo Switch games, the mean price for a new game is $54.97. Assume the population has a standard deviation of $48.43. (Source: PriceCharting) 38. Tornadoes per Month From a random sample of 35 months from January 2006 through December 2020, the mean number of tornadoes per month in the United States was about 100. Assume the population standard deviation is 111. (Source: NOAA) 39. In Exercise 35, would it be unusual for the population mean to be over $1500? Explain. 40. In Exercise 36, would it be unusual for the population mean to be over $90? Explain. 41. In Exercise 37, does it seem likely that the population mean could be greater than $70? Explain. 42. In Exercise 38, does it seem likely that the population mean could be less than 100? Explain.
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