brett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20…

Answer:

A. -5.30

Explanation:

Step1: Recall z - statistic formula

$z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$ where $\bar{x}$ is sample mean, $\mu$ is population mean, $\sigma$ is population standard deviation, and $n$ is sample size.

Step2: Identify given values

$\bar{x} = 295$, $\mu=310$, $\sigma = 20$, $n = 50$

Step3: Substitute values into formula

$z=\frac{295 - 310}{\frac{20}{\sqrt{50}}}$ First, calculate denominator: $\frac{20}{\sqrt{50}}\approx\frac{20}{7.071}\approx2.83$. Then, calculate numerator: $295-310=- 15$. So, $z=\frac{-15}{2.83}\approx - 5.30$.