In: Math
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.
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 \(4.50 .\)