Question

Suppose you want to estimate the proportion of traditional college students on your campus who own their own car. From research on other college​ campuses, you believe the proportion will be near 20​%. What sample size is needed if you wish to be 99​% confident that your estimate is within 0.02 of the true​ proportion?

Answer 1

Answer:

2,655 students

Step-by-step explanation:

The z-score for a 99% confidence interval is z = 2.576

The standard error for a proportion p is:

$SE = z*\sqrt{\frac{p*(1-p)}{n} }$

For a proportion of p =0.20, in order to ensure a standard error of 0.02, the sample size 'n' must be:

$0.02 = 2.576*\sqrt{\frac{0.2*(1-0.2)}{n}}\\n=2,654.31$

Rounding up to the next whole student, the sample size needed is 2,655 students.