a researcher collated data on americans leisure time activities. she found the mean number of hours spent…

a researcher collated data on americans leisure time activities. she found the mean number of hours spent watching television each weekday to be 2.7 hours with a standard deviation of 0.4 hours. jonathan believes that his football team buddies watch less television than the average american. he gathered data from 15 football teammates and found the mean to be 2.3. which of the following shows the correct z - statistic for this situation?\n-3.87\n-0.26\n3.23\n5.22

a researcher collated data on americans leisure time activities. she found the mean number of hours spent watching television each weekday to be 2.7 hours with a standard deviation of 0.4 hours. jonathan believes that his football team buddies watch less television than the average american. he gathered data from 15 football teammates and found the mean to be 2.3. which of the following shows the correct z - statistic for this situation?\n-3.87\n-0.26\n3.23\n5.22

Answer

Explanation:

Step1: Recall the z - statistic formula for sample mean

The formula for the z - statistic of a 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 given in the problem

We are given that $\mu = 2.7$ (population mean), $\sigma=0.4$ (population standard deviation), $\bar{x} = 2.3$ (sample mean), and $n = 15$ (sample size).

Step3: Substitute the values into the formula

$z=\frac{2.3 - 2.7}{\frac{0.4}{\sqrt{15}}}$. First, calculate the denominator: $\frac{0.4}{\sqrt{15}}\approx\frac{0.4}{3.873}\approx0.1033$. Then, calculate the numerator: $2.3−2.7=- 0.4$. Now, divide the numerator by the denominator: $z=\frac{-0.4}{0.1033}\approx - 3.87$.

Answer:

-3.87