Question

brett is performing a hypothesis test in which the population mean is 310 and the standard deviation is 20. his sample data has a mean of 295 and a sample size of 50. which of the following correctly depicts the z - statistic for brett’s data?
-5.30
-0.11
4.28
6.27

Explanation:

Step1: Recall z - statistic formula

The formula for the z - statistic in a hypothesis test for the sample mean 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 the values

We are given that $\bar{x} = 295$, $\mu=310$, $\sigma = 20$, and $n = 50$.

Step3: Substitute the values into the formula

First, calculate the denominator $\frac{\sigma}{\sqrt{n}}=\frac{20}{\sqrt{50}}\approx\frac{20}{7.071}\approx2.828$.
Then, calculate the numerator $\bar{x}-\mu=295 - 310=- 15$.
Finally, calculate the z - statistic $z=\frac{-15}{2.828}\approx - 5.30$.

Answer:

-5.30