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.
This solution gives the step by step method for computing confidence interval for estimating population proportion and mean.