Question

Earlier, we considered data from the GSS on numbers of close friends people reported having. The mean for this variable is 7.44, with a standard deviation of 10.98. Let's say that you decide to use the GSS data to test whether people who live in rural areas have a different mean number of friends than does the overall GSS sample. Again, treat the overall GSS sample as the entire population of interest. Let's say that you select 40 people living in rural areas and find that they have an average of 3.9 friends. What is the z statistic for this sample

Answer 1

Answer:

The z statistic for this sample is -2.04.

Step-by-step explanation:

The null hypothesis is:

$H_{0} = 7.44$

The alternate hypotesis is:

$H_{1} \neq 7.44$

The z-statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the population mean(the hypothesis tested), $\sigma$ is the standard deviation and n is the size of the sample.

In this problem:

$X = 3.9, \mu = 7.44, \sigma = 10.98, n = 40$. So

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{3.9 - 7.44}{\frac{10.98}{\sqrt{40}}}$

$z = -2.04$

The z statistic for this sample is -2.04.