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: Identify the formula for z - statistic

The formula for the z - statistic in a sampling distribution of 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 given values

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

Step3: Substitute the values into the formula

$z=\frac{2.3 - 2.7}{\frac{0.4}{\sqrt{15}}}$. First, calculate the denominator: $\sqrt{15}\approx3.873$, and $\frac{0.4}{\sqrt{15}}=\frac{0.4}{3.873}\approx0.103$. Then, calculate the numerator: $2.3−2.7=- 0.4$. So, $z=\frac{-0.4}{0.103}\approx - 3.87$.

Answer:

-3.87