# Another bonus question - testing the means?

• Dec 12th 2009, 08:59 AM
mecia
Another bonus question - testing the means?
Hi all,

here is another of the bonus questions we had to choose from. I think I want to compare the difference between means (Ho = 24, Ha not = 24), but I am not sure what to do and the second half of the question has really been bothering me. I am realy interested in how to solve this. Thanks

The question:

72 students enroll in different sections of a course. Test the hypothesis that people do not care what professor is teaching when they choose a course. Test the hypothesis that Prof. c is preferred by 20% of all students and that the rest are evenly split between Porfs A and B. Which fits better, doe either fit well at all?

Prof A - 25 students

Prof B - 28 students

Prof C - 19 Students
• Dec 12th 2009, 08:33 PM
Ond
I think you should be looking for testing proportions in this example, not means.

In the first example you should test whether the proportion is evenly spread out between the three professors (i.e. 33,33% for each professor) given the information you have.

In the second example you should test whether the proportion is 20% for Prof. C, 40% for Prof. B and 40% for Prof. A.

So, you have three H0 in the first example and three H0 in the second example. If you can reject more H0's in example 1 than in example 2 for instance (using the same critical value in all H0's of course), then I would have thought that example 2 is the better way, and vice versa. But I'm not quite sure if I'm entirely correct regarding that.

Another way could be that you find the average of the three p-values in example 1 and then in example 2 and see which one is lower. But then again, I'm not quite sure.
• Dec 27th 2009, 10:07 PM
CaptainBlack
Quote:

Originally Posted by Ond

In the second example you should test whether the proportion is 20% for Prof. C, 40% for Prof. B and 40% for Prof. A.

So, you have three H0 in the first example and three H0 in the second example. If you can reject more H0's in example 1 than in example 2 for instance (using the same critical value in all H0's of course), then I would have thought that example 2 is the better way, and vice versa. But I'm not quite sure if I'm entirely correct regarding that.

Another way could be that you find the average of the three p-values in example 1 and then in example 2 and see which one is lower. But then again, I'm not quite sure.

Wrong, the question requires a $\chi^2$-test with null hypothesis that the frequencies are $28.8$, $28.8$ and $14.4$ for profs A, B and C, with $2$ degrees of freedom.

CB