97. Suppose that an accounting firm does a study to determine the time needed to complete one person's tax forms. It randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The population distribution is assumed to be normal. a. i. ac ii. O = iii. n b. In words, define the random variables X and X . c. Which distribution should you use for this problem? Explain your choice. d. Construct a 90% confidence interval for the population mean time to complete the tax forms. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. e. If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make? f. If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why? g. Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within one hour. How would the number of people the firm surveys change? Why?Use the following information to answer the next ten exercises: A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was 2.2 pounds with a standard deviation of 0.1 pounds. The population standard deviation is known to be 0.2 pounds. 13. Identify the following: a. = b. 0= c. n = 14. In words, define the random variable X. 15. In words, define the random variable X. 16. Which distribution should you use for this problem? 17. Construct a 90% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound. 18. Construct a 95% confidence interval for the population mean weight of the heads of lettuce. State the confidence interval, sketch the graph, and calculate the error bound. 19. In complete sentences, explain why the confidence interval in Exercise 8.17 is larger than in Exercise 8.18Use the following information to answer the next seven exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. 6. Identify the following: a. x b. o c. n = 7. In words, define the random variables X and X. 8. Which distribution should you use for this problem? 9. Construct a 90% confidence interval for the population mean time to complete the forms. State the confidence interval, sketch the graph, and calculate the error bound. 10. If the Census wants to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make? 11. If the Census did another survey, kept the error bound the same, and surveyed only 50 people instead of 200, what would happen to the level of confidence? Why? 12. Suppose the Census needed to be 98% confident of the population mean length of time. Would the Census have to survey more people? Why or why not?8.1 A Single Population Mean using the Normal Distribution 95. Among various ethnic groups, the standard deviation of heights is known to be approximately three inches. We wish to construct a 95% confidence interval for the mean height of male Swedes. Forty-eight male Swedes are surveyed. The sample mean is 71 inches. The sample standard deviation is 2.8 inches. a. i. = ii. o = iii. n = b. In words, define the random variables X and X. c. Which distribution should you use for this problem? Explain your choice. d. Construct a 95% confidence interval for the population mean height of male Swedes. i. State the confidence interval. ii. Sketch the graph. iii. Calculate the error bound. e. What will happen to the level of confidence obtained if 1,000 male Swedes are surveyed instead of 48? Why?Search this book Q My high 8.1 A Single Population Mean using the Normal Distribution Use the following information to answer the next five exercises: The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds. 1. Identify the following: a. x = b. 0 = c. n = 2. In words, define the random variables X and X. 3. Which distribution should you use for this problem? 4. Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval, sketch the graph, and calculate the error bound. 5. What will happen to the confidence interval obtained, if 500 newborn elephants are weighed instead of 50? Why ? Use the following information to answer the next seven exercises: The U.S. Census Bureau conducts a study to determine the time needed to complete the short form. The Bureau surveys 200 people. The sample mean is 8.2 minutes. There is a known standard deviation of 2.2 minutes. The population distribution is assumed to be normal. 6. Identify the following