Use a 0.05 significance level and conduct a full hypothesis test. List the null and alternative hypotheses, the z-score, the P-value, and whether to reject or not reject the null hypothesis. Round z-scores to the nearest tenth.

In tests of a computer component, it is found that the mean time between failures is 937 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 960 hours, with a standard deviation of 52 hours. Test the claim that for the modified components, the mean time between failures is greater than 937 hours.