Question

A national measure of religiosity is measured for all undergraduate students who attend private religious based universities in the United States. The scores are approximately normally distributed with a mean of 80 and a standard deviation of 10. Seton Hill University measured an incoming freshman class (300 students) to identify if the religiosity of SHU students is significantly different from that of the entire private religious based university undergraduate student population. In the SHU freshman class a sample mean of 91 was obtained (M = 91). Compute the one sample z test to decide whether to reject or retain the null hypothesis at a 0.05 level of significance (a = .05).

15a. State the null and alternative (research) hypotheses.

15b. What type of tailed test is this? State the testing criteria.

15c. Compute the test statistic for this research (z statistic).

15d. State whether to reject or retain the null hypothesis.

15e. What is the p-value associated with the z statistic?

15f. What summary conclusion can you make about SHU students compared to the overall private/religious affiliated student population?

Answer 1

First we summarize the data given to us as follows:

Sample mean, m = 91

Standard deviation, S = 10

Sample size, n = 300

The hypotheses are stated as follows:

H0: = 80

Ha: 80

Now we calculate the test statistic:

z = (m-80)/(S/(n^0.5)) = (91-80)/(10/(300^0.5)) = 19.05

This is a two tailed hypothesis test.

The corresponding p-value for this z-statistic, as obtained from a cumulative z-table is:

p = 0 (approx.)

Since p-value is almost equal to zero, so we have to reject the null hypothesis.

Thus, the summary conclusion is that based on the given data, the religiosity of SHU students is significantly different from that of the entire private religious based university undergraduate student population.