Consider the following hypothesis test:
$H_0: \mu ≤ 20$
$H_1: \mu>20$
A sample of 81 produced a sample mean of 20.55. The population standard deviation is 3. The value of the test statistic is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) - 1.65
$z = \frac{\bar{x} - \mu}{\sigma/\sqrt{n}}$
$= \frac{20.55 - 20}{3/\sqrt{81}}$
$= \frac{0.55}{3/9}$
$= \frac{0.55}{\frac{1}{3}}$
$= 0.55 \times 3 = 1.65$
The value of the test statistic is $1.65$.