In each part, we have given the value obtained for the test statistic, $z$, in a one-mean $z-$test. We have also specified whether the test is two tailed, left tailed, or right tailed. Determine the $P-$value in each case and decide whether, at the $5\%$significance level, the data provide sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

a. $z=-1.25$; left-tailed test

b. $z=2.36$; right-tailed test

c. $z=1.83$; two-tailed test

The value obtained for the test statistic, $z$, in one-mean$z-$test.
The tests have been specified to be left-tailed, right-tailed and two-tailed respectively.

The test static,$z=-1.25$ , which is left-tailed test.
$P-$value $=P(Z\le z)$

$=P(Z\le -1.25)$

The test static,$z=2.36$ , which is right-tailed test.
$P-$value $=P(Z\ge z)$

$=P(Z\ge 2.36)$

$=1-0.9909$

The test static, $z=1.83$, which is two-tailed test.

$P-$value$=2P(Z\ge z)$
role="math" localid="1651240615811" $=2P(Z\ge 1.83)$

$=2[1-P(Z<1.83\left)\right]$

$=2[1-0.9664]$

$=2(0.0336)$

$=0.0672$