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, 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. It is known that the standard deviation of the population is 9 hours. a.

Give the null and the alternative hypotheses.
b.

Compute the test statistic.
c.

At the 1% level of significance using the critical value approach, test management's belief. What is the p-value and your conclusion?