Consider the following hypothesis test :
\(H_0: \mu \le 35\)
\(H_a: \mu \gt 35\)
A sample of 25 provided a sample mean of 34.25. The population standard deviation is 3. The value of the test statistic is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → −1.25
The population standard deviation is known, so the test statistic for the mean is
\( \displaystyle z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} \)
with \(\bar{x} = 34.25\), \(\mu_0 = 35\) (the value in \(H_0\)), \(\sigma = 3\), n = 25:
\( \displaystyle \frac{\sigma}{\sqrt{n}} = \frac{3}{5} = 0.6 \)
\( \displaystyle z = \frac{34.25 - 35}{0.6} = \frac{-0.75}{0.6} = -1.25 \)
The value is negative because the sample mean is below 35.