Next time you get gas, note that each pump should have been inspected by some local authority such as the City of Columbus. This is to prevent businesses from giving you less than you have been sold. 12 samples were taken from a local gas station. In each case, the pump read exactly 1 gallon. Assuming the amount of gas dispensed is normally distributed. The samples were carefully measured and found to actually contain, in gallons: 0.92, 1.00, 0.98, 0.95, 0.96, 1.03, 1.01, 0.96, 0.90, 0.95, 0.96, 1.00 a) Suppose the variance is known to be of = 0.001 gallons squared. Find a 99% confidence interval for , the true mean amount of gas dispensed. b) Suppose the variance is unknown. Find a 99% confidence interval for u. c) Interpret your confidence interval from the perspective of a consumer watchdog. That is, if you worked for the Franklin County Auditor, do you believe this gas pump needs attention? d) Suppose there are 113 gas stations in Columbus. 29 were found to have some violation in a safety . inspection. Use the central limit theorem to compute a 99% confidence interval for p, the true proportion is gas stations with a violation. Describe the sampling distribution you use. e) Repeat part d, but compute an Agresti-Coull confidence interval for p. Compare and contrast the two intervals. f Interpret your confidence intervals from the perspective of a consumer watchdog