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. Assume from past information that it is known that thestandard deviation of the populationis 9 hours.

a.

Give the null and the alternative hypotheses.

b.

Compute the test statistic.

c.

What is thep-value associated with the sample results?

d.

At 99% confidence test management's belief. State your conclusion in the context of the problem.