Question

A data set includes data from student evaluations of courses. The summary statistics are n=80​, x overbar =4.39​, s =2.29. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.50. 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

Here,

Sample mean \(=\bar{x}=4.39\)

Sample \(S . D=s=2.29\)

Sample size \(=n=80\)

Degrees of freedom \(=\mathbf{7 9}\)

Significance Level \(=\alpha=0.05\)

Step 1:

\(H_{0}: \mu=4.5\)

\(H_{1}: \mu \neq 4.5\) (Two tailed test)

Step 2:

The test statistic is,

Step 3:

\(P-\) value \(=P(|t|>-0.430)=0.6684\)

Step 4: Conclusion:

Since the \(P\) -value is greater than the significance level, we fail to reject \(H_{0}\).

There is not sufficient evidence to reject the claim that population of student course evaluations has a mean equal to \(4.50 .\)