Question

There are 21,000 students. Each student tests the fairness of a coin (yes, the same coin; the instructor somehow gets Tyche’s help in getting the coin to each student in turn). Specifically, each student tests:

Null: p is equal to 0.5 Alternative: p is not equal to 0.5

using the 5% cutoff.
Suppose that, unknown to the students, the coin is in fact fair.

1. The expected number of students whose test will conclude that the coin is unfair is __________.

Answer 1

@amistre64

Answer 2

you still around?

Answer 3

well, 5% of the students are expected to get an unfair result .. if im reading it right

Answer 4

Yes, this is the question
1. The expected number of students whose test will conclude that the coin is unfair is __________. [This answer is actually an integer, cleanly calculated; but I’ll allow you an error of +-5.]

Answer 5

using a 5% cutoff rate ... that implies a 95% interval for the number of fairs; and 5% for unfairs

Answer 6

what is 5% of the total number of kids?

Answer 7

the confidence interval would amount to what:\[.50\pm1.96\sqrt{\frac{.5*.5}{21000}}\]

Answer 8

@amistre64 This may help.

There are N students who take the course, the cutoff is 5% (on the normal curve this is 2.5% on each side). The cutoff can be thought as 5% of the students will end up thinking that the coin is unfair. What you are really doing is putting all the students under the normal curve and the ones who get it wrong are at the two ends of the normal curve i.e. the tail. so Number of students x cutoff [%] = Number of students who get it wrong.

Answer 9

:) yep

Answer 10

So the result is? ;)

Answer 11

1050 is the correct ans

Answer 12

You are correct!!!

Answer 13

Thank you @jaysmittt @amistre64 @Social