Consider the following hypothesis test.
\(H_0: \mu \le 12\)
\(H_a: \mu \gt 12\)
If a sample of 25 is taken with sample mean 15 and a sample standard deviation of 6, then the value of t-test statistic is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{5}{2}\)
For a test about a population mean with the sample standard deviation s, the one-sample t statistic is
\( \displaystyle t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}} \)
Here \(\bar{x} = 15\), \(\mu_0 = 12\), s = 6 and n = 25:
\( \displaystyle t = \frac{15 - 12}{6/\sqrt{25}} = \frac{3}{6/5} = \frac{15}{6} = \frac{5}{2} \)