Question

In a survey on download music The Gallup Poll asked 700 internet users, if they ''user downloaded music from an internet site that was not authorized by record company, or not '' and 18% responded ''yes''

a) Estimate the true proportion of internet users who have downloaded music from an internet site that was not authorized with 95 confidence.

b) What sample size is recorded if you wish to 90% confidence that your estimation is within 0,01 of the true proportion ?

Answer 1

Answer

(A) proportion given is 18% or 18/100 = 0.18

sample size is n = 700

formula for the confidence interval is given as

where z = 1.96 for 95% confidence interval (using z distribution table)

setting the given values, we get

on solving, we get

So, required 95% confidence interval is (0.1515, 0.2085)

(B) we know that the formula for the required sample size is given as

where p= 0.18, margin of error= ME = 0.01 and z = 1.64 for 90% confidence interval (using z distribution table)

setting the given values, we get

Rounding it off to nearest whole number, we get sample size n = 3970