Chapter 9, Problem 1PS

If you use a 0.005 level of significance in a two-tail hypothesis test, what decision will you make if $Z_{\text{STAT}}=-0.76?$

To determine

Determine whether to reject or accept a two-tailed hypothesis when $Z_{STAT}=-0.76$ at a level of significance of 0.05.

Answer to Problem 1PS

The two-tailed hypothesis cannot be rejected.

Explanation of Solution

According to the provided information, the level of significance is 0.05, that is, $\alpha =0.05$ and the critical values of the test statistics of the two-tailed hypothesis are 1.96 and $-1.96$ .

The rejection region is given by:

$Z_{STAT}>1.96\text{or }{Z}_{STAT}<-1.96$

The acceptance or non-rejection region is given by:

$-1.96\le Z_{STAT}\le 1.96$

It given by $Z_{STAT}=-0.76$ . Since,

$-1.96\le -0.76\le 1.96$

There is insufficient evidence to reject the two-tailed hypothesis.