Question

A data set includes data from student evaluations of courses. The summary statistics are n=96​, x overbarx=3.91​, s=0.66

Use a 0.01 significance level to test the claim that the population of student course evaluations has a mean equal to 4.00. Assume that a simple random sample has been selected. Identify the null and alternative​ hypotheses, test​statistic, P-value, and state the final conclusion that addresses the original claim.

Answer 1

We have to test the hypothesis regarding the student evaluations of courses, and we have given the information for a random sample of students evaluations of courses with sample mean and with the sample standard deviation of . The population mean course evaluation is given as .

The null and alternative hypothesis with given significance level of is:

i.e., the population mean of student course evaluation is equal to 4.

i.e., the population mean of student course evaluation is different than 4.

Test-statistic:

Degrees of freedom:

So, the test-statistic is calculated as

P-value: Since it is a two-tailed hypothesis, so the p-value for the calculated test statistic is calculated as-

So, the p-value is calculated as

Decision:

Since,

Conclusion: Since we fail to reject the null hypothesis, so we conclude that "At the sample data does not provide enough evidence to support the alternative hypothesis."

In other words, at we fail to reject null hypothesis, i.e., , so we conclude that the population mean of student course evaluation is not different than 4.