Consider the following hypothesis test:
\( \mathrm{H}_{0}:\ \mu=17 \)
\( \mathrm{H}_{a}:\ \mu\ne 17 \)
A sample of 25 provided a sample mean \( \overline{x}=18 \) and a population standard deviation S = 2.5, then the value of the t-test statistic is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
The t statistic for a sample mean is
\( \displaystyle t=\frac{\overline{x}-\mu_{0}}{S/\sqrt{n}} \)
\( \displaystyle =\frac{18-17}{2.5/\sqrt{25}} \)
\( \displaystyle =\frac{1}{0.5} \)
\( \displaystyle =2 \)
The question calls 2.5 the population standard deviation but writes it as S; the statistic uses 2.5 in the same place either way, so its value is 2.