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Chapter 6: Q110SE (page 330)
Calculate the finite population correction factor for each
of the following situations:
a. n = 50, N = 2,000
b. n = 20, N = 100
c. n = 300, N = 1,500
a.0.9876
b. 0.8989
c. 0.8947
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USGA golf ball tests. The United States Golf Association (USGA) tests all 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 called "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 to within 1 yard with 90% confidence. Assume that
past tests have indicated that 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?
Improving SAT scores. Refer to the Chance (Winter 2001) and National Education Longitudinal Survey (NELS) study of 265 students who paid a private tutor to help them improve their SAT scores, Exercise 2.88 (p. 113). The changes in both the SAT鈥揗athematics and SAT鈥揤erbal scores for these students are reproduced in the table. Suppose the true population meansa change in score on one of the SAT tests for all students who paid a private tutor is 15. Which of the two tests, SAT鈥揗athematics or SAT鈥揤erbal, is most likely to have this mean change? Explain.
U.S. Postal Service鈥檚 performance. The U.S. Postal Service (USPS) reports that 95% of first-class mail within the same city is delivered on time (i.e., within 2 days of the time of mailing). To gauge the USPS performance, Price Waterhouse monitored the delivery of first-class mail items between Dec. 10 and Mar. 3鈥攖he most difficult delivery season due to bad weather conditions and holidays. In a sample of 332,000 items, Price Waterhouse determined that 282,200 were delivered on time. Comment on the performance of USPS first-class mail service over this time period.
It costs you \(10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of \)1,500.
a. Do you have sufficient funds to estimate the population mean for the attribute of interest with a 95% confidence interval 5 units in width? Assume.
b. If you used a 90% confidence level, would your answer to part a change? Explain.
Latex allergy in health care workers. Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Each sample of 46 hospital employees who were diagnosed with a latex allergy based on a skin-prick test reported their exposure to latex gloves (Current Allergy& Clinical Immunology, March 2004). Summary statistics for the number of latex gloves used per week is ,
s = 11.9.
a. Give a point estimate for the average number of latex gloves used per week by all health care workers with a latex allergy.
b. Form a 95% confidence interval for the average number of latex gloves used per week by all health care workers with a latex allergy.
c. Give a practical interpretation of the interval, part b.
d. Give the conditions required for the interval, part b, to be valid.
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