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10. A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5.1%). What is the point estimate of the mean percentage of reservations that are canceled on the day of the flight?
Solution: The point estimate of the mean percentage of reservations is the midpoint of the interval, which is (1.3% + 5.1%)/2 = 3.2%
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11. 45 CEO's from the electronics industry were randomly sampled and a 90% confidence interval for the avg. of all electronics CEO's was constructed. THE interval was ($95,136, $110,372). Give the practical interpretation of the interval above.
Solution: The interval means that there’s a 90% probability that the actual population mean salary belongs to the interval ($95,136, $110,372).
12. The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hr. period.
He randomly selects 64 different 24-hour periods and determines the number of admissions for each.
Sample mean: 15.4
S2 = 16
Estimate the mean number of admissions per 24-hr. period with a 99% confidence interval.
Solution: The 99% confidence interval is
13. A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. Approximately how large a sample do the buyers need in order to insure that they are 90% confident that the margin of error is within 5%?
Solution: The 90% margin of error is given by
We want that the margin of error is within 5%
(because
) Therefore, the sample size is
.
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