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

7.4

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

7.6

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

7.4

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

0.05

. Assume that

=

0.5

hours.

A.H0

:

=7.6

hours

H1

:

>7.6

hours

=0.05

=z2.57

P

-value

=0.0050

Reject

H0

. At the

5%

significance level, the data provide sufficient evidence to conclude that the mean running time of all light bulbs,

, has increased from the previous mean of

7.6

hours.

B. H0

:

=7.6

hours

H1

:

>7.6

hours

=0.05

=z2.53

P

-value

=0.0057

Reject

H0

. At the

5%

significance level, the data provide sufficient evidence to conclude that the mean running time of all light bulbs,

, has increased from the previous mean of

7.6

hours.

C. H0

:

=7.4

hours

H1

:

>7.4

hours

=0.05

=z2.57

P

-value

=0.0050

Reject

H0

. At the

5%

significance level, the data provide sufficient evidence to conclude that the mean running time of all light bulbs,

, has increased from the previous mean of

7.4

hours.

D. H0

:

=7.4

hours

H1

:

>7.4

hours

=0.05

=z2.53

P

-value

=0.0057

Reject

H0

. At the

5%

significance level, the data provide sufficient evidence to conclude that the mean running time of all light bulbs,

, has increased from the previous mean of

7.4

hours.