1.The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.15 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months.

Find thep-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.

a. Round your answer to four decimal places.

p=

b. Will you reject the null hypothesis at=0.025?

2.Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed and vary slightly. It is known that when the machine is working properly, the mean length of the rods is 36 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.035 inch. The quality control department at the company takes a sample of 20 such rods every week, calculates the mean length of these rods, and tests the null hypothesis,=36

inches, against the alternative hypothesis,36

inches. If the null hypothesis is rejected, the machine is stopped and adjusted. A recent sample of 20 rods produced a mean length of 36.015 inches.

Calculate thep-value for this test of hypothesis. Based on thisp-value, will the quality control inspector decide to stop the machine and adjust it if he chooses the maximum probability of a Type I error to be 0.025?

a. Use the normal distribution table. Round your answer to four decimal places.

p-value =

b.The machine? (does not need or needs adjustment.)