Question

 

Are Male Professors and Female Professors Rated Differently? Listed below are student evaluation scores of female professors and male professors from Data Set 17 “Course Evaluations” in Appendix B. Test the claim that female professors and male professors have the same mean evaluation ratings. Does there appear to be a difference?

Females 4.4 3.4 4.8 2.9 4.4 4.9 3.5 3.7 3.4 4.8

Males      4.0 3.6 4.1 4.1 3.5 4.6 4.0 4.3 4.5 4.3

Answer 1

The values provided in the above problem is as belows

Females: 4.4 3.4 4.8 2.9 4.4 4.9 3.5 3.7 3.4 4.8

Males : 4.0 3.6 4.1 4.1 3.5 4.6 4.0 4.3 4.5 4.3

Ho : The female professors and male professors have the same mean evaluation ratings.

H1: The female professors and male professors have not the same mean evaluation ratings

Using Parameter

We consider the variables

X = Female sample observations

Y = Male sample observations

n1= Total number of Female observations = 10

n2= Total number of male observations = 10

We use the test statistic is

.....................(1)

and Sample variances of the samples of Females and Males

0.56

Using all values in equation (1)

The test statistic t = -0.3152

We write test statistic

So, the critical value of t with 18 degrees of freedom is 2.10

Calculated value of test statistic t < critical value of t

So we accept null hypothesis Ho. that is

The female professors and male professors have the same mean evaluation ratings.