Question

A music industry researcher wants to estimate, with a 90% confidence level, the proportion of young urban people (ages 21 to 35 years) who go to at least 3 concerts a year. Previous studies show that 21% of those people (21 to 35 year olds) interviewed go to at least 3 concerts a year. The researcher wants to be accurate within 1% of the true proportion. Find the minimum sample size necessary.

Answer 1

21378

Explanation:

The confidence level is 90%, which gives us a Z of 1.645.

Our equation is (Z^2*p*q)/e^2

(1.645^2*p*(1-.21))/ (.01^2)

E is the error proportion, .01

Q is 1-p or the proportion

P is the pop you need

With this, we can solve

and get p = 21377.5975 and rounded to 21378