Misapplication of Hypothesis Testing?

I was asked the following question and would like to hear your view:

"In the year 2005 National exam, 57.4% of the students who sat for the mathematics paper obtained grade A. A private teacher claims that his record is superior, because 65 out of his 100 students who took the same exam obtained grade A.
1. Is his claim justified at the 2% level of significance?
2. What is the smallest level of significance at which his claim would be justified?"

I feel that there is not enough information to carry out such a test, for the simple reason that the population consists of groups of students who took private tuition and obtained grade A (call this group X), as well as those who did not take private tuition and obtained A (call this group Y). The sample proportion of 0.65 should be compared with the proportion of grade A within X but not with the population proportion 0.574. But information on the proportion within X is missing. Therfore no meaningful comparison could be made.
I would say tentatively that the claim is not justified. Intuitively, the private teacher has a small sample size and because of this the statistic he or she gives is likely to vary. Two percent level of significance is high.

Test and Confidence Interval for One Proportion

Test of p = 0.574 vs p not = 0.574
Sample      X      N  Sample p        95.0 % CI       P-Value
1          65    100  0.650000  (0.548151, 0.742706)    0.130


TS Contributor
There is enough information to test the teacher's hypothesis, but as macro90 has shown, the hypothesis was not supported....

All the teacher is claiming is that his/her students' rate of "A" grades is higher than the national average - a valid claim if it can be shown that it is significant.
Thanks to your quick response!

I forgot to emphasise that it is not clear what the question wants:
Is it comparison between the private teacher's record with that of the national average, or with that of all the unknown private teachers?

If it is the first case then we do have enough information to carry out a test (whether the test is significant is purely a technical matter).

If it is the latter, I think we do not have enough information because we are not told the national average of the record of all the private teachers. However, I tend to favor the second intepretation of the question because we should be comparing apple for apple.


TS Contributor
I see your points - in the "real world" these are valid criticisms - but if this is just a homework assignment, then I wouldn't worry about it too much...:D
Misaaplication of Hypothesis Testing

I am sorry that's exactly what I was concerned about. We are talking about potential misapplication here.


TS Contributor
OK, well if this is in fact a real-world application, then your concerns are justified - however, convincing someone that they are "wrong" is very difficult to do, even with seemingly "strong" statistical evidence, or another philosophical viewpoint...

Good luck.
Misappliation of Hypothesis Testing?

Huh isn't this the job of the mathematician? If there is a misapplication then he needs to point it out. Whether "the person" is convinced is another matter. I think in maths we are looking for logic and precision.


TS Contributor
We just provide advice and a professional opinion here.....it's up to you to solve your problems.:)

In my professional career I've presented mountains of evidence, both in favor of and against certain "practices," but at the end of the day, it's up to the decision-maker to do what they ultimately want to do....

Yes, I agree that math and statistics involve logic and precision, but we also have to deal with people, who, for the most part, make decisions based on emotion...

....sometimes they go against your advice.

That's all I'm going to say on this matter....