Consider the following hypothesis test:
\( \mathrm{H_0}:\ \mu\le 35 \)
\( \mathrm{H_a}:\ \mu\gt 35 \)
A sample of 25 provided a sample mean of 34.65. The population standard deviation is 4. The value of the t-test statistic is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → −0.4375
The population standard deviation \( \sigma=4 \) is given, so the standard error of the mean is \( \frac{\sigma}{\sqrt{n}} \). The test statistic (called t in the question) is
\( \displaystyle t=\frac{\bar{x}-\mu_0}{\sigma/\sqrt{n}} \)
Here \( \bar{x}=34.65 \), \( \mu_0=35 \), \( \sigma=4 \), n = 25:
\( \displaystyle \frac{\sigma}{\sqrt{n}}=\frac{4}{5}=0.8 \)
\( \displaystyle t=\frac{34.65-35}{0.8} \)
\( \displaystyle t=\frac{-0.35}{0.8}=-0.4375 \)