Two researchers, Joe and Bob, work together to study the proportion of students

Question

Two researchers, Joe and Bob, work together to study the proportion of students at their college who support recycling on campus. They find that the sample proportion of students who say they support recycling is 0.76. They each construct a confidence interval based on this sample proportion. Joe comes up with (0.73, 0.81) while Bob gets (0.70, 0.82). Which interval has to be wrong? Joe's interval is wrong Bob's interval is wrong there is no way to know without sample size and confidence level Explain why.

Explanation / Answer

For sample proportion p =0.76

For compute confidence interval we have the formula

p +/- Z value *S.E. ( S.e. = sqrt((P(1-P))/n)

To calculate z value we want confidence level.

To calculate S.E. We want a sample size

so if we want to know which interval is correct,

We should at least have one of the sample size or confidence level.

So we can calculate S.E. and then give a correct confidence interval.

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