Consider the following test:

$Η_0=μ ≤12$
$H_a= μ > 12$

A sample of 36 provided a sample mean $\bar x = 16$ and a sample standard deviation $S=4.2$. Then the value of the t-test statistic is:

5.71

The correct answer is Option (4) → 5.71

Given:

$H_0: \mu \le 12, \ H_a: \mu > 12$

Sample size: $n=36$, sample mean: $\bar{x}=16$, sample standard deviation: $S=4.2$

t-test statistic formula:

$t = \frac{\bar{x} - \mu_0}{S/\sqrt{n}}$

Substitute values:

$t = \frac{16 - 12}{4.2 / \sqrt{36}} = \frac{4}{4.2 / 6} = \frac{4}{0.7} \approx 5.714$

$\text{Answer: } t \approx 5.714$