Question

It was reported that 31.62% of high school students in a metropolitan area regularly smoke marijuana. If school administrators would like to estimate the proportion of students at their school who regularly smoke marijuana, how large a sample should be selected so that the margin of error is + 4% with a level of confidence of 98%? n=

Answer 1

Given that, estimate of the population proportion (p) = 0.3162

margin of error (E) = 0.04

A 98% confidence level has significance level of 0.02 and critical value is, $Z_{\alpha/2} = 2.33$

We want to find, the sample size (n)

n=p*(1 – p) * -per2 ) 2 0.3162 * (1 – 0.3162) * 2.33. 0.04 733.6397 => n 734

=> n = 734

Note : If we used critical value = 2.326 then required sample size is n = 731