Question

A university is comparing the grade point averages of theater majors with the grade point averages of history majors. The university currently has 50 total theater majors and 50 total history majors. The mean and standard deviation for each population are shown in the table.

Theater Majors - (Population Mean 3.22 , Population Standard Deviation 0.002)

History Majors - (Population Mean 3.24 , Population Standard Deviation 0.08)

The university wants to test whether there is a significant difference in GPAs for students in the two majors. What is the P-value and conclusion at a significance level of 0.05?

Answer 1

Using the z-distribution, as we have the standard deviation for the population, we have that the correct option is:

The p-value is of 0.0772. Fail to reject the null hypothesis that there is no difference in the GPA's.

What are the hypothesis tested?

At the null hypothesis, we test if there is no difference in the means, that is:

$H_0: \mu_T - \mu_H = 0$

At the alternative hypothesis, we test if there is a difference, that is:

$H_1: \mu_T - \mu_H \neq 0$

What is the distribution of the sampling distribution of sample differences?

For each sample, we have that:

$\mu_T = 3.22, s_T = \frac{0.002}{\sqrt{50}} = 0.00028284271$

$\mu_H = 3.24, s_H = \frac{0.08}{\sqrt{50}} = 0.01131370849$

Hence:

$\overline{x} = \mu_T - \mu_H = 3.22 - 3.24 = -0.02$

$s = \sqrt{s_T^2 + s_H^2} = \sqrt{0.00028284271^2 + 0.01131370849^2} = 0.0113$

What is the test statistic?

It is given by:

$z = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis, hence:

$z = \frac{\overline{x} - \mu}{s}$

$z = \frac{0.02 - 0}{0.0113}$

$z = -1.77$

What is the p-value and the decision?

Using a z-distribution calculator, considering a two-tailed test, as we are testing if the mean is different of a value, with z = -1.77, it is found that the p-value is of 0.0772.

Since the p-value is greater than the significance level of 0.05, the correct option is:

The p-value is of 0.0772. Fail to reject the null hypothesis that there is no difference in the GPA's.

More can be learned about the z-distribution at https://brainly.com/question/13873630

Answer 2

Answer:

The P-value is 0.0772. Fail to reject the null hypothesis that there is no difference in the GPAs.