Consider the following hypothesis test:
$H_0:μ=15$
$H_a:μ≠ 15$
A sample of 50 provided a sample mean of 14.15. If the sample standard deviation is 3, then the value of the test statistic in t-test is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -2 **
Given:
Sample mean = $14.15$
Population mean under $H_0$ = $15$
Sample standard deviation = $3$
Sample size = $50$
t-statistic formula:
$t = \frac{\bar{x} - \mu_0}{\frac{s}{\sqrt{n}}}$
Compute denominator:
$\frac{s}{\sqrt{n}} = \frac{3}{\sqrt{50}} = \frac{3}{7.071} = 0.4243$
Now compute t:
$t = \frac{14.15 - 15}{0.4243}$
$t = \frac{-0.85}{0.4243}$
$t \approx -2.003$
The value of the t-statistic is approximately −2.003.