Consider the following test:
\(H_0: \mu \le 12\)
\(H_a: \mu \gt 12\)
A sample of 36 provided a sample mean \(\bar x = 16\) and a sample standard deviation \(S=4.2\). Then the value of the t-test statistic is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5.71
The population standard deviation is not known, so the one-sample t statistic uses the sample standard deviation S:
\( \displaystyle t = \frac{\bar{x} - \mu_0}{S/\sqrt{n}} \)
Here \(\mu_0 = 12\), \(\bar{x} = 16\), S = 4.2 and n = 36:
\( \displaystyle \frac{S}{\sqrt{n}} = \frac{4.2}{6} = 0.7 \)
\( \displaystyle t = \frac{16 - 12}{0.7} = \frac{4}{0.7} \approx 5.71 \)