1. Kate and Leopold are thinking about-buying the Rockwood Motel located on Interstate 70. Before they make up their mind, they want to estimate the average number of vehicles that go by the motel each day in the summer. Fortunately, the highway department has been counting vehicles on 1-70 near the motel. A random sample of 36 summer days shows a mean of 16,000 cats per day with a standard deviation of 2400 cars. Find a 75% confidence interval for the population mean number of cars per summer day going past the Rockwood Motel. Verbalize your result?
2. Andre is the head waiter at a famous gourmet restaurant in San Francisco. The Internal Revenue Service is doing an audit on his tax return this year In particular, the IRS wants to know the average amount Andre gets for a tip. In an effort to satisfy the IRS, Andre took a random sample of 8 credit card receipts, each of which had his tip recorded. The results were as follows:
$10.00 $11.93 $15.70 $9.10
$12.75 $11.15 $14.50 $13.65
Find a 90% confidence interval for all tips received by Andre, using this sample.
3. Suppose, that 800 students were selected at random from student bodies at different colleges across the nation and given flu shots. All 800 students were then exposed to the flu, and 600 of them did not get the flu. Find a 99% confidence interval for the true proportion of all students whose flu shots would be successful in preventing them from getting the flu. Verbalize this revelation
4. A certain company makes light fixtures on an assembly line. An efficiency expert wants to determine the mean time if takes an employee to assemble the switch on one of these futures. A preliminary study used a random sample of 45 observations and found that the sample standard deviation was s = 78 seconds. How many more observations are necessary for the efficiency expert to be 95% sure that the point estimate x¯ will be in error from the true mean p by at most 15 seconds?