Claim: The mean systolic blood pressure of all healthy adults is less than than $125 \mathrm{~mm} \mathrm{Hg}$. Sample data: For 257 healthy adults, the mean systolic blood pressure level is $124.75 \mathrm{~mm} \mathrm{Hg}$ and the standard deviation is $15.78 \mathrm{~mm} \mathrm{Hg}$. The null and alternative hypotheses are $\mathrm{H}_{0}: \mu=125$ and $\mathrm{H}_{1}: \mu<125$. Find the value of the test statistic. The value of the test statistic is (Round to two decimal places as needed.)

Step 1 ：We are given that the sample mean (\(\bar{X}\)) is 124.75, the population mean under the null hypothesis (\(\mu\)) is 125, the standard deviation of the population (\(\sigma\)) is 15.78, and the sample size (\(n\)) is 257.

Step 2 ：We can use these values to calculate the test statistic using the formula: \[Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{n}}\]

Step 3 ：Substituting the given values into the formula, we get: \[Z = \frac{124.75 - 125}{15.78 / \sqrt{257}}\]

Step 4 ：Solving the above expression, we find that the value of the test statistic (\(Z\)) is approximately -0.25.

Step 5 ：Final Answer: The value of the test statistic is \(\boxed{-0.25}\).