Question

A data set includes data from student evaluations of courses.

Answer 1

Answer:

We fail to reject the null hypothesis at the significance level of 0.05.

Step-by-step explanation:

We have a larga sample size of n = 80, $\bar{x} = 4.39$ and s = 2.29. We want to test

$H_{0}: \mu = 4.50$ vs $H_{1}: \mu \neq 4.50$ (two-tailed alternative)  

Because we have a large sample, our test statistic is

$Z = \frac{\bar{X}-4.50}{s/\sqrt{n}}$ which is normal standard approximately. We have the observed value

$z_{0} = \frac{4.39-4.50}{2.29/\sqrt{80}} = -0.4296$.

The p-value is given by 2P(Z < -0.4296) = (2)(0.3337) = 0.6674 (because of the simmetry of the normal density)

With the significance level $\alpha = 0.05$, we fail to reject the null hypothesis because the p-value is greater than 0.05.