Consider the following hypothesis test.
$H_0:μ≤ 12$
$H_a:μ> 12$
If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → $\frac{5}{2}$
Given$H_0: \mu \le 12$, $H_a: \mu > 12$
Sample size: $n = 25$, sample mean: $\bar{x} = 15$, sample standard deviation: $s = 6$
t-test statistic formula:
$t = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}$
Substitute values:
$t = \frac{15 - 12}{6 / \sqrt{25}} = \frac{3}{6/5} = \frac{3}{1.2} = 2.5$