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 :
Answer & explanation
Correct answer: option 1
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: $Z=-2.25$