# Problem 403

[talexpage]

A film developer claim that the mean number of pictures developed for a camera with 27 exposures is less than 26. If a hypothesis test is performed, how should you interpret a decision that

(a)    Reject the null hypothesis ?

(b)   Fails to reject the null hypothesis ?

Solution

(a)    Begin by determining the claim of the hypothesis test.

The claim is µ < 26.

Next determine whether the claim is the null hypothesis or the alternative hypothesis. The null hypothesis, , is a statistical hypothesis that contains a statement of equality, whereas the alternative hypothesis, . Contain a statement of strict inequality.

Since the claim contain a statement of strict inequality, µ < 26, it is the alternative hypothesis.

When a null hypothesis is rejected, there is sufficient evidence that the null hypothesis is false and enough evidence to support alternative hypothesis. Thus, since the claim is the alternative hypothesis, there is enough evidence to support the claim that the mean number of pictures developed for a camera with 27 exposures is less than 26.

(b)   As in part (a), begin by determining the claim of the hypothesis test and determine whether it is the null or alternative hypothesis. Note that you have already found that the claim of the hypothesis test is µ < 26 and that it is the alternative hypothesis.

When you fail to reject the null hypothesis, there is insufficient evidence that the null hypothesis is false and not enough evidence to support the alternative hypothesis. Thus, since the claim is the alternative hypothesis, there is not enough evidence to support the claim that the mean number of picture developed for a camera with 27 exposures is less than 26.