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.

Answer

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Answer

$\boxed{z = 6}$ is the value of the standardized z-test statistic

Steps

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