5.70 USGA golf ball test. The United States Golf Association USGA tests al new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine call "Iron Byron" a name inspired by the swing of the famous golfer Byron Nelson. Suppose the USGA wishes to estimate the mean distance for a new brand within 1 year with 90% confidence. Assume that part tests have indicated the the standard deviation of the distances Iron Byron hits golf balls is approximately 10 yards. How many golf balls should be hit by Iron Byron to achieve the desired accuracy in estimating the mean?
5.86 In each of the following instances, determine whether you would use a s- or t- statistic (or neither) to form a 90% confidence interval and then look up the appropriate z- or t- value.
a. Random sample of size n = 23 from a normal distribution with unknown mean and standard deviation.
b. Random sample of size n = 135 from a normal distribution with unknown mean and standard deviation.
c. Random sample of size n = 10 from a normal distribution with unknown mean and standard deviation of 5.
d. Random sample of size n = 73 from a distribution about which nothing is known.
e. Random sample of size n = 12 from a distribution about which nothing is known.
5.92 Semester hours taken by CPA candidates. Refer to the Journal of Accounting and Public Policy (Spring 2002) study of 100,000 first-time candidates for the CPA exam. The mean number of semester hours of college credit taken by the candidates was 141.31 hours. The standard deviation was reported to be 17.77 hours.
a. Compute a 99% confidence interval for the mean number of semester hours taken by all first-time candidates for the CPA exam.
b. Give a practical interpretation of the interval, part a.
c. For the interpretation, part b, to be valid, what conditions must hold?
5.98 Sick leave taken by employees. A company is interested in estimating u, the mean number of days of sick leave taken by all its employees. The firm's statistician selects at random 100 personnel files and notes the number of sick days taken by each employee. The following sample statistics are computed: xbar = 12.2 days, s = 10 days.
a. Estimate u using a 90% confidence interval. Interpret the results.
b. How many personnel files would the statistician have to select in order to estimate u within 2 days with a 99% confidence interval?
a. Since the sample size, n < 30, we shall use t-statistic.
Degrees of freedom, df = n-1 = 23-1 = 22
t-value = 2.069
b. Since the sample size, n > 30, we shall use z-statistic.
z-value = 1.96
c. Since the sample size, n < 30, we shall use t-statistic.
Degrees of ...