# Math Help - Sample Size & Confidence Interval

1. ## Sample Size & Confidence Interval

I need someone to help me with the problem listed below. I have read and re-read it and I don't think we can complete this problem with the information given because of the unknown number of students in the university. Am I right?

Preliminary estimates suggest that about 58% of students at a state university favor implementing an honor code. To obtain a 95% confidence interval of the proportion of all students at the university favoring the honor code, what is the minimum sample size needed if the total width of the confidence interval must be less that 5 percentage points (i.e. the confidence interval should extend at most 2.5 percentage points above the below the sample proporation)?

2. We don't know the size of the sample for the preliminary estimate, either.

With a little thought, perhaps we can get past it.

$n\;=\;\frac{1.96^{2}*0.58*0.42}{0.025^{2}}$

This estimate, 1,497 seems like a HUGE number. It may be, but in the absence of additional information, that may be the choice.

1,497/0.05 = 30,000 or so. If the university is big enough, 1,497 is not so bad. It's not like we're conducting destructive experiments or asking lots of questions. 1,500 surveys on the street is not so bad. It could take a while, and I'm not sure how you would control duplicates, but why not.