Consider the following hypothesis test:

$H_0:μ≤12$

$H_a : μ > 12$

A sample of 25 provided a sample mean $\bar x = 14$ and a sample standard deviation $S = 4.32$. Compute the value of the test statistic.

2.31

The correct answer is Option (1) → 2.31

Given $n = 25, \bar x = 14, S = 4.32, μ_0= 12$

$t =\frac{\bar x-μ_0}{S/\sqrt{n}}=\frac{14-12}{4.32/\sqrt{25}}$

$=\frac{10}{4.32}= 2.31$

$∴ t = 2.31$

and degrees of freedom $= 25-1 = 24$