[Objective: Understand the hypothesis test of the mean] Suppose a consumer product

researcher wanted to find out whether a Sharpie lasted longer than the manufacturer's claim

that their Sharpies could write continuously for a mean of 14 hours. The researcher tested 40

Sharpie's and recorded the number of continuous hours each Sharpie wrote before drying up.

Test the hypothesis that Sharpies can write for more than a mean of 14 continuous hours.

Following are the summary statistics:

hours,

hours. Use an

=

14.5

=

1.2

=

0.05

significance level.

Follow and answer the following accordingly.

a.

Set-up the null and alternative hypotheses. Write in correct notation. Specify if left-

tailed, right-tailed or two-tailed test.

b. Specify the significance level . Sketch your critical or rejection region.

c.

Gather your evidence. Specify the information derived from the sample.

d. Compute the appropriate test statistic.

e. Compute the critical value (classical approach)

f.

Compute the p-value (p-value approach)

g.

Decision criterion: Based on (e) or (f), specify your decision if reject or do not reject the

null hypothesis.