Perform a one-sample

z

-test for a population mean using the

P

-value approach. Be sure to state the hypotheses and the significance level, to compute the value of the test statistic, to obtain the

P

-value, and to state your conclusion.

In the past, the mean running time for a certain type of flashlight battery has been

8.7

hours. The manufacturer has introduced a change in the production method which he hopes has increased the mean running time. The mean running time for a random sample of

40

light bulbs was

8.9

hours. Do the data provide sufficient evidence to conclude that the mean running time of all light bulbs,

, has increased from the previous mean of

8.7

hours? Perform the appropriate hypothesis test using a significance level of

0.05

. Assume that

=

0.5

hours.