Confidence interval for mean and proportion for Highway Patrol

11. As part of a safety check, the Pennsylvania Highway Patrol randomly stopped 65 cars and checked their tire pressure. The sample mean was 32 pounds per square inch with a sample standard deviation of 2 pounds per square inch. Develop a 98 percent confidence interval for the population mean.

12. A survey of 4,000 college graduates determines that the mean length of time to earn a bachelor's degree is 5.08 years and the standard deviation is 1.89 years. Construct a 96 percent confidence interval for the mean time required for all graduates to earn a bachelor's degree.

13. Suppose the college in question 12 has only graduated 10,000 students. Construct a 96 percent confidence interval for the mean time required for all graduates to earn a bachelor's degree.

14. A manufacturer of diamond drill bits for industrial production drilling and machining wishes to investigate the length of time a drill bit will last while drilling carbon steel. The production of the drill bits is very expensive, thus the number available for testing is small. A sample of 8 drill bits had a mean drilling time of 2.25 hours with a standard deviation of 0.5 hours. Construct a 95 percent confidence interval for the population mean. Is it reasonable for the manufacturer to claim that the drill bits will last 2.5 hours?

15. Of a random sample of 90 firms with employee stock ownership plans, 50 indicated that the primary reason for setting up the plan was tax related. Develop a 90 percent confidence interval for the population proportion of all such firms with this as the primary motivation.