Use the foiiowing information to answer the next five exercises. A hospital is trying to cut down on emergency room wait times. It is interested in the amount of time patients must wait before being called back to be examined. An investigation committee randomly surveyed 70 patients. The sample mean was 1.5 hours with a sample standard deviation of 0.5 hours. 38. Identify the following: a. 5': : b. 33 : c. n : d. n 1 : 39. Define the random variables X and X in words. 40. Which distribution should you use for this problem? 41. Construct a 95% confidence interval for the population mean time spent waiting. State the confidence interval, sketch the graph, and calculate the error bound. 42. Explain in complete sentences what the confidence interval means. Use the fotlowing information to answer the next 13 exercises: The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks] from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X : the number of colors on a national flag. X Freq. 1 1 2 ? 3 18 4 T 5 6 Table 8.10 49. Calculate the following: a. C = b. ST = C. n= 50. Define the random variable X in words. 51. What is @ estimating? 52. Is Or known? 53. As a result of your answer to Exercise 8.52 , state the exact distribution to use when calculating the confidence interval. Construct a 95% confidence interval for the true mean number of colors on national flags. 54. How much area is in both tails (combined)? 55. How much area is in each tail? 56. Calculate the following: a. lower limit b. upper limit c. error bound 57. The 95% confidence interval is58. Fill in the blanks on the graph with the areas, the upper and lower limits of the Confidence Interval and the sample mean. Figure 8.9 59. In one complete sentence, explain what the interval means. 60. Using the same 52', 33, and level of confidence, suppose that n were 69 instead of 39. Would the error bound become larger or smaller? How do you know? 61. Using the same 5:, 33, and n : 39, how would the error bound change if the confidence level were reduced to 90%? Why