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 \(\boxed{-3.57}\).