Last year, the mean running time for a certain type of light bulb was 8.5 hours. This year, the manufacturer has introduced a change in the production method. A random sample of 40 of the new light bulbs has a mean running time of 8.7 hours with a standard deviation, s, of 0.5 hours. At the 0.05 significance level, test the claim that the mean running time of the new light bulbs is greater than last year’s mean of 8.5 hours. a) State the null and alternative hypotheses symbolically. b) Which test procedure is appropriate to perform the required hypothesis test? c) Compute the value of the test statistic. d) Determine the P-value or provide the rejection region. Please round your answers to three decimal places. e) Should you reject the null hypotheses or not? f) What is your conclusion about the hypothesis test?