Question

A data set includes data from student evaluations of courses. The summary statistics are n = 84, x (x bar) = 4.16, s = 0.59. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. 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. Show your work. Correct Answers are in BOLD (how did I get these without using excel).

What are the null and alternative hypotheses? H0: M=4.25, H1: M≠4.25

Determine the test statistic. -1.40

Determine the P-value. 0.166

State the final conclusion that addresses the original claim: (1) H0. There is (2) evidence population of student course evaluations is equal to 4.25 (3)

to conclude that the original claim that the mean of the correct.

(1) Fail to reject or Reject

(2) Sufficient or Not Sufficient

(3) Is or Is Not

Answer 1

We need to test the claim is that the population of student course evaluations has a mean equal to 4.25. So, the null hypothesis (claim) and alternative hypothesis (negation of claim) is,

H0: M=4.25, H1: M≠4.25

Standard error of mean, SE = s /  = 0.59 /  = 0.06437427762

Test statistic, t = ( - M) / SE =  (4.16 - 4.25) / 0.06437427762 = -1.398073941 -1.40

Degree of freedom = n-1 = 84-1 = 83

For two-tail test, p-value = 2 * p(t < -1.398073941, df = 83) =  0.1658 0.166

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0.

There is not sufficient evidence at 5% significance level to conclude that the true mean student course evaluations is not 4.25