Probability Formula for Testing Joe's Claim in a Statistics Class

[doug123]

Joe thinks that no more than 20% of students in his statistics class will get an A in the final examination. To prove his claim, he takes a random sample of 35 students and finds to his surprise that 30% of his students got an A. At a .01 percent level of significance can we reject Joe's view?

I do not want the answer to this question, I would just like to know what formula to use, and why. Thank you so much I really appreciate it.

 

[BicycleTree]

Are we to assume that the total size of Joe's class is very large? If his class only has 40 students in it that would affect the result.

 

[doug123]

no he has 35 students in his class, I put that in the question, however I am curious as to the formula to use

 

[BicycleTree]

No, you said he took a random sample of 35 students. If he only HAS 35 students then you can say with certainty that more than 20% of his students got A's.

 

[doug123]

okay i really don't understand what your saying, all i want to know is what equation to use that's all. Thanks

 

[DaveC426913]

Doug, the way you phrased your question "...he takes a random sample of 35 students ..." suggests that his SAMPLE contains 35 students and that the size of the class is unspecified.

If I may reword:


"Joe thinks that no more than 20% of students in his statistics class will get an A in the final examination. To prove his claim, he takes a random sample (eg. n=5 or n=10) from the 35 students in the class and finds to his surprise that 30% of his students got an A. At a .01 percent level of significance can we reject Joe's view?

He took ".

 

[doug123]

NO, he took a random sample OF 35 students, not he took a random sample from 35 students. So to explain this he basically took 35 students and found that 30% of those 35 students got an A. It isn't that difficult to understand. If anyone knows the formula to use I would appreciate it. Thanks for all of your help anyway though.

 

[BicycleTree]

Doug, there is no formula for that because the question is incomplete. You have to either assume that his class size is very large, or you have to say how large it actually is.