Consider the following hypothesis test:
$H_0: μ = 18$
$H_1:μ≠ 18$,
If a sample of 48 provided a sample mean $\bar x = 17$ and a sample standard deviation $σ=4.5$, then the value of the t-test statistic is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -1.54
Given:
H0: μ = 18, H1: μ ≠ 18
Sample size: n = 48
Sample mean: x̄ = 17
Sample standard deviation: σ = 4.5
t-test statistic formula:
$t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$
Substitute the values:
$t = \frac{17 - 18}{4.5 / \sqrt{48}}$
$t = \frac{-1}{4.5 / 6.9282}$
$t = \frac{-1}{0.649}$
$t \approx -1.54$
Therefore, the t-test statistic value is approximately -1.54