Consider the following hypothesis test :
\(H_0: \mu \le 16\)
\(H_a: \mu \gt 16\)
A sample of 49 provided a sample mean of 15.25. The population standard deviation is 2. The value of the test statistic is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −2.625
The population standard deviation is known, so the test uses the z statistic with the hypothesised mean \(\mu_0 = 16\):
\( \displaystyle z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} \)
The standard error is
\( \displaystyle \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{49}} = \frac{2}{7} \)
So
\( \displaystyle z = \frac{15.25 - 16}{2/7} \)
\( \displaystyle = -0.75 \times \frac{7}{2} \)
\(= -2.625\)