1:A manufacturer of Maserati cars wishes to investigate the length of time a car will last while driving over 200 mph. The production of Maseratis is very expensive, thus the number available for testing is small. A sample of 8 cars had a mean driving time of 2.25 hours with a standard deviation of 0.5 hours.

a. What is the population mean? What is the best estimate of that value?

b. Construct a 95 percent confidence interval for the population mean.

c. Explain why the t distribution is used as a part of the confidence interval.

d. Is it reasonable for the manufacturer to claim that the cars will last 2.5 hours?

14. In a survey, 858 out of 2,600 lottery players said they expected to win sometime in the next 12 months. Construct a 90% confidence interval for "winning" in the next 12 months.

2:Sports Illustrated, a magazine for sports enthusiasts, would like to report the mean amount earned by rookies (first year players) in their particular sport. How large a sample is required if the 95 percent level of confidence is used and the estimate is to be within $2,500? The standard deviation is $16,000.

3:Read the news story below. Using the 95% confidence level, what sample size would be needed to estimate the true proportion of stores selling cigarettes to minors with an error of 3%? The Tri-Cities Tobacco Reduction coalition recently sent three underage teenagers out to see whether they could buy cigarettes from stores in Detroit and Highland Park. The results were not good. Of the 320 stores checked, 82 sold cigarettes to the teens, which were between the ages of 15 & 17. People must be 18 to legally buy cigarettes in Michigan. When the age of the buyers is not clear, the retailer is supposed to check the buyers ID. The stores that sold the cigarettes will face fines