Consider the following hypothesis test:-
\(H_0: \mu = 20\)
\(H_a: \mu \ne 20\)
A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -2.1
The one-sample t statistic is
\( \displaystyle t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} \)
with \(\bar{x} = 19\), \(\mu_0 = 20\), \(s = 3\) and \(n = 40\):
\( \displaystyle \frac{s}{\sqrt{n}} = \frac{3}{\sqrt{40}} = \frac{3}{6.325} = 0.474 \)
\( \displaystyle t = \frac{19 - 20}{0.474} = -2.11 \)
So \(t \approx -2.1\). It is negative because the sample mean is below the hypothesised mean.