Question: In tests of a computer component, it is found that the mean time between failures is 530 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures.

518 548 561 523 536 499 538 557 528 563

a. Determine the mean and standard deviation for the data set. (5 points)

b. At the 0.01 level of significance, test the claim that for the modified components, the mean time between failures is greater than 530 hours. You may assume the time between failures is normally distributed. (5 points)