inclass-ch8

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Boston College *

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HMKT230-1

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Statistics

Date

Apr 3, 2024

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docx

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Uploaded by SargentWorldSkunk23

_ 2. A simple random sample of 50 items from a population with o = 6 resulted in a sample mean of 32. a. Provide a 90% confidence interval for the population mean. b. Provide a 95% confidence interval for the population mean. c. Provide a 99% confidence interval for the population mean. 8. Studies show that massage therapy has a variety of health benefits and it is not too expen- sive (The Wall Street Journal, March 13, 2012). A sample of 10 typical one-hour massage therapy sessions showed an average charge of $59. The population standard deviation for a one-hour session is o0 = $5.50. a. What assumptions about the population should we be willing to make if a margin of error is desired? b. Using 95% confidence, what is the margin of error? c. Using 99% confidence, what is the margin of error? 12. Find the 7 value(s) for each of the following cases. a. Upper tail area of .025 with 12 degrees of freedom Lower tail area of .05 with 50 degrees of freedom Upper tail area of .01 with 30 degrees of freedom Where 90% of the area falls between these two f values with 25 degrees of freedom Where 95% of the area falls between these two r values with 45 degrees of freedom o a0 o

_ 14. A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased? 26. The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $3.94 (US EIA website, April 6, 2012). The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. a. The desired margin of error is $.10. b. The desired margin of error is $.07. c. The desired margin of error is $.05. - - - -— 40. For many years businesses have struggled with the rising cost of health care. But recently, the increases have slowed due to less inflation in health care prices and employees paying for a larger portion of health care benefits. A recent Mercer survey showed that 52% of U.S. employers were likely to require higher employee contribu- tions for health care coverage in 2009. Suppose the survey was based on a sample of 800 companies. Compute the margin of error and a 95% confidence interval for the proportion of companies likely to require higher employee contributions for health care coverage in 2009.

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