1.The quality control manager at the Aladin Light factory needs to estimate the mean life of a large shipment of light bulbs. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours.

a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. ___________________________

b. Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment. ___________________________

c. Construct a 90% confidence interval estimate for the population mean life of light bulbs in this shipment. ___________________________

d. Construct an 80% confidence interval estimate for the population mean life of light bulbs in this shipment. ___________________________

e. Discuss your observation every time there is a change in confidence level. ___________________________

2.ABC insurance company handling malpractice cases is interested in estimating the average amount of claims against physicians of a certain specialty. The company obtains a random sample of 80 claims and finds = Php15,250 and s = Php3,542.

a. Give a 95% confidence interval for the average amount of a claim. _____________________________

b. Give a 99% confidence interval for the average amount of a claim. _____________________________________

3.Your manager in the ABC thinner supply store wants you to estimate the actual amount of thinner contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of thinner is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of thinner per 1-gallon can is 0.990 gallon.

a. Construct a 99% confidence interval estimate for the sample mean amount of thinner included in a 1-gallon can. ________________________________

b. Based on these results, do you think that the manager has a right to complain to the manufacturer? Why? _____________________________________________________________________

c. Must you assume that the sample amount of thinner per can is normally distributed here? Explain. _____________________________________________________________________

d. What will happen if you reduce the confidence level to 95% and 90%? What could be the reason? _____________________________________________________________________