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Chapter 6: Q7E (page 339)
Explain the difference between an interval estimator and a point estimator for
A random variable is an estimator, as well as a value, is an estimation that represents the estimator's calculated number.
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Shopping on Black Friday. The day after Thanksgiving— called Black Friday—is one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of Retail and Distribution Management (Vol. 39, 2011). One question was, “How many hours do you usually spend shopping on Black Friday?” Data for the 38 shoppers are listed in the accompanying table.
a. Describe the population of interest to the researchers.
b. What is the quantitative variable of interest to the researchers?
c. Use the information in the table to estimate the population mean number of hours spent shopping on Black Friday with a 95% confidence interval.
d. Give a practical interpretation of the interval.
e. A retail store advertises that the true mean number of hours spent shopping on Black Friday is 5.5 hours. Can the store be sued for false advertising? Explain.
The following sample of 16 measurements was selected from a population that is approximately normally distributed:
Study of aircraft bird-strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comment on the accuracy of this estimate. Use a 95% confidence interval to support your inference.
U.S. Postal Service’s 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—the 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.
A random sample of size n = 225 yielded = .46
a. Is the sample size large enough to use the methods of this section to construct a confidence interval for p? Explain.
b. Construct a 95% confidence interval for p.
c. Interpret the 95% confidence interval.
d. Explain what is meant by the phrase “95% confidence interval.”
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