Consider the following hypothesis test:
\(H_0: \mu \le 16\)
\(H_a: \mu \gt 16\)
A sample of 25 provided a sample mean \(\bar{x} = 17\) and a sample standard deviation \(s = 3.5\), then the value of the test statistic in t-test is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1.43
For a one-sample t-test with sample standard deviation s,
\( \displaystyle t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} \)
Here \(\bar{x} = 17,\ \mu_0 = 16,\ s = 3.5,\ n = 25\):
\( \displaystyle t = \frac{17 - 16}{3.5/\sqrt{25}} \)
\( \displaystyle = \frac{1}{0.7} \approx 1.43 \)