dion is performing a hypothesis test in which the population mean is 92 and the standard deviation is 2. his…

Explanation:

Step1: Recall z - statistic formula

The formula for the z - statistic in a one - sample z - test is $z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size.

Step2: Identify given values

We are given that $\mu = 92$, $\sigma=2$, $n = 7$, and $\bar{x}=93.5$.

Step3: Substitute values into formula

$z=\frac{93.5 - 92}{\frac{2}{\sqrt{7}}}=\frac{1.5}{\frac{2}{\sqrt{7}}}$. First, calculate $\frac{2}{\sqrt{7}}\approx\frac{2}{2.646}\approx0.756$. Then, $z=\frac{1.5}{0.756}\approx1.98$.

Answer:

1.98