The following is a set of hypotheses, some information from one or more samples, and a standard error from a randomization distribution. Test $H_{0}: \mu=77$,vs $H_{a}: \mu>77$ when the sample has $n=22, \bar{x}=81.2$, and $s=3.4$ with $S E=0.7$. Find the value of the standardized $z$-test statistic. Round your answer to two decimal places.

Step 1 ：Given in the problem: sample mean (\(\bar{x}\)) = 81.2, population mean (\(\mu\)) = 77, and standard error (SE) = 0.7

Step 2 ：The standardized z-test statistic is calculated using the formula: \(z = \frac{\bar{x} - \mu}{SE}\)

Step 3 ：Substitute the given values into the formula: \(z = \frac{81.2 - 77}{0.7}\)

Step 4 ：Calculate the above expression: \(z = \frac{4.2}{0.7}\)

Step 5 ：\(\boxed{z = 6}\) is the value of the standardized z-test statistic