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A sample mean, sample size, and population standard deviation are provided below. Use the one-mean z-test to perform the required hypothesis test at the $5 \%$ significance level.
\[
\bar{x}=22, n=39, \sigma=7, H_{0}: \mu=26, H_{a}: \mu< 26
\]

The test statistic is $z=$
(Round to two decimal places as needed.)

Step 1 ：Given that the sample mean \(\bar{x}\) is 22, the population mean \(\mu\) is 26, the population standard deviation \(\sigma\) is 7, and the sample size \(n\) is 39.

Step 2 ：The formula for the test statistic for a one-mean z-test is \(z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}\).

Step 3 ：Substitute the given values into the formula: \(z = \frac{22 - 26}{7 / \sqrt{39}}\).

Step 4 ：First, calculate the denominator: \(\frac{7}{\sqrt{39}} = 1.12\) (rounded to two decimal places).

Step 5 ：Then, calculate the numerator: \(22 - 26 = -4\).

Step 6 ：Finally, divide the numerator by the denominator to get the z-score: \(z = \frac{-4}{1.12} = -3.57\) (rounded to two decimal places).

Step 7 ：So, the test statistic is \(\boxed{-3.57}\).