Consider the following hypothesis test :
\(H_o:\mu\le 24\)
\(H_a:\mu\gt 24\)
A sample of 64 provided a sample mean of 24.3. The population standard deviation is 2. The value of the test statistic is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1.2
The population standard deviation is known, so the test statistic for the mean is
\( \displaystyle z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}} \)
Here \(\bar{x} = 24.3\), \(\mu_0 = 24\), \(\sigma = 2\), \(n = 64\).
\( \displaystyle \frac{\sigma}{\sqrt{n}} = \frac{2}{\sqrt{64}} = \frac{2}{8} = 0.25 \)
\( \displaystyle z = \frac{24.3 - 24}{0.25} = \frac{0.3}{0.25} = 1.2 \)
The value of the test statistic is 1.2.