Consider the following hypothesis test :

$H_o: \mu ≤ 30 $

$H_a: \mu > 30 $

A sample of 81 provided a sample mean of 29.25. The population standard deviation is 3. The value of the test statistic is :

-2.25

Given:

$\mu_{0}=30,\;\bar{x}=29.25,\;\sigma=3,\;n=81$

Test statistic:

$Z=\frac{\bar{x}-\mu_{0}}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{29.25-30}{\frac{3}{\sqrt{81}}}$

$Z=\frac{-0.75}{\frac{3}{9}}$

$Z=\frac{-0.75}{\frac{1}{3}}$

$Z=-2.25$

final answer: $Z=-2.25$