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:

1.65

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 $1.65$.