Question

A data set includes data from student evaluations of courses. The summary statistics are n=85, x =3.41 , s=0.61. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. 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. What are the null and alternative hypotheses?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 3.50

H_a :    3.50

= 3.41

= 3.50

s = 0.61

n = 85

Test statistic = z

= ( - ) / s / n

= (3.41 - 3.50) / 0.61 / 85

= -1.36

Test statistic = -1.36

P(z < -1.36) = 0.0869

P-value = 2 * 0.0869 = 0.1738

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not enough evidence to suggest that the population of student course evaluations has a mean equal to 3.50 .