The McCollough Corporation, a producer of various kinds of batteries, has been producing "D" size batteries with a life expectancy of 87 hours. Due to an improved production process, the management believes that there has been an increase in the life expectancy of their "D" size batteries. A sample of 36 batteries showed an average life of 88.5 hours. Assume from past information that it is known that the standard deviation of the population is 9 hours.
Use a 0.01 level of significance to test for the evidence of improvement in the life expectancy of the batteries. Use the critical value criterion in your decision making.
[Hint: You need to (1) write the null and alternative hypotheses (2) know the significance level of the test (3) write the appropriate formula for the test-statistic (4) using the sample data, compute the numerical value of the test-statistic (5) look up the critical value, and finally (6) draw your conclusion].
What is the p-value of the test? Draw your conclusion using the p-value criterion.