Consider the following hypothesis test
\(H_0 : \mu \ge 16\)
\(H_1 : \mu \lt 16\)
A sample of 36 provided a sample mean of 15.4. The population standard deviation is 3. The value of the test statistic ‘t’ is,
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −1.2
The test compares the sample mean with \(\mu_0 = 16\), the value in \(H_0\). With the population standard deviation \(\sigma = 3\) given, the test statistic is
\( \displaystyle t = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} \)
Here \(\bar{x} = 15.4\), n = 36, so \(\sqrt{n} = 6\):
\( \displaystyle t = \frac{15.4 - 16}{3/6} \)
\( \displaystyle = \frac{-0.6}{0.5} \)
\(= -1.2\)
The value is negative because the sample mean is below 16.