1. A random sample of the number of hours worked by 40 employees has a mean of 29.6 hours worked. Assume the population standard deviation is 7.9 hours. Using a 95% confidence level, find the margin of error, E, for the mean number of hours worked. In a study of 265 subjects, the average score on the examination was 63.8. Assume o = 3.08. What is a 95% confidence interval for u? 3. A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 20 students, the mean age is found to be 22.9 years. From past studies, the standard deviation is known to be 1.5 years, and the population is normally distributed. Construct a 90% confidence interval of the population mean age. 4. The weight of a product is measured in pounds. A sample of 50 units is taken from a batch. The sample yielded the following results: x = 75 lbs., and o = 10 1bs. Calculate a 99% confidence interval for u. 5. What sample size is needed to estimate with 90% confidence the mean intake of calcium within 20 units of the true mean if the intake is normal with a variance of 1900 units? 6. When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? a Increase in the level of confidence. b. Increase in the sample size. C. Increase in the population standard deviation.7. A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of cheese. The estimate must be within 0.5 milligram of the population mean. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 2.8 milligrams. b. Repeat part (a) using a 99% confidence interval. c. Which level of confidence requires a larger sample size? Explain. 8. Mary is a waitress at Seventh Heaven Burgers. She wants to estimate the mean amount each group at a table leaves a tip. A random sample of 42 tables had a mean of x = $7.30. Based on long term experience, o is known to be about $2.92. Round final answers to nearest cent. a. Find a 90% confidence interval for the average amount left by all groups. b. Use part a to estimate an interval of dollar values for Mary's total tips for a shift with 42 tables. . Find ta/2 for a. a 95% confidence interval when sample size is 18. b. a 99% confidence interval when sample size is 38. C. a 90% confidence interval when sample size is 64. 10. Consider a 90% confidence interval for u. Assume o is not known. For which sample size, n = 10 or n = 20 a. Is the critical value to/2 larger? Is the confidence interval longer? 11. Lorraine computed a confidence interval for u based on a sample size of 41. Since she did not know o, she used s in her calculations. Lorraine then used the normal distribution for the confidence interval instead of a Student's t distribution. Was her interval longer or shorter than one obtained with an appropriate Student's t distribution? Explain.12. At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years A.D. for an archeological excavation site (Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo, edited by Kohler, Washington State University): 1189 1271 1267 1272 1268 1316 1275 1317 1275 Assume the population follows a normal distribution. a. Verify that the sample mean x ~ 1272 with a standard deviation s ~ 37 years. b. Find a 90% confidence interval for the mean of all tree-ring dates from this archaeological site. Round the lower and upper bounds to the nearest year. c. Explain the meaning of the confidence interval. 13. A sample of 8 items has an average fat content of 18.6 grams and a standard deviation of 2.4 grams. Assuming a normal distribution, construct a 99 percent confidence interval for u