Question 2, 10.3.3
HW Score: $0 \%, 0$ of 9 points
Part 1 of 4
Points: 0 of 1
To test $\mathrm{H}_{0}: \mu=40$ versus $\mathrm{H}_{1}: \mu< 40$, a random sample of size $\mathrm{n}=22$ is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below.
Click here to view the t-Distribution Area in Right Tail.
(a) If $\bar{x}=37.5$ and $s=13.4$, compute the test statistic.
$t_{0}=\square$ (Round to three decimal places as needed.)

Step 1 ：We are given that the sample mean \(\bar{x} = 37.5\), the hypothesized population mean \(\mu_0 = 40\), the sample standard deviation \(s = 13.4\), and the sample size \(n = 22\).

Step 2 ：We are testing the hypotheses \(\mathrm{H}_{0}: \mu=40\) versus \(\mathrm{H}_{1}: \mu<40\).

Step 3 ：The test statistic for a t-test can be calculated using the formula: \(t_0 = \frac{\bar{x} - \mu_0}{s / \sqrt{n}}\).

Step 4 ：Substituting the given values into the formula, we get \(t_0 = \frac{37.5 - 40}{13.4 / \sqrt{22}}\).

Step 5 ：Solving the above expression, we find that the test statistic \(t_0 = -0.875\).

Step 6 ：\(\boxed{-0.875}\) is the final answer.