In tests of a computer component, it is found that the mean time between failures is

940

hours. A modification is made which is supposed to increase reliability by increasing the time between failures. Tests on a sample of

36

modified components produce a mean time between failures of

986

hours. Using a

5%

level of significance, perform a hypothesis test to determine whether the mean time between failures for the modified components is greater than

940

hours. Assume that the population standard deviation is

51

hours.