Question

A market research analyst wishes to know how large a sample of the homes in a certain community to draw in order to find out what proportion of the homes with at least one member who has seen a certain newspaper advertisement. There are 500 homes in the community. The analysts wants to be within 0.04 of the true proportion with 90% confidence. In a pilot sample of 20 homes, 35% of the respondents indicated that someone in the home had seen the advertisement. How large a sample should be drawn?

Answer 1

Solution:

We are given

Margin of error = E = 0.04

Confidence level = 90%

Estimate for proportion = p = 0.35

q = 1 – p = 1 – 0.35 = 0.65

Critical Z value = 1.6449

(by using z-table)

The sample size formula is given as below:

n = p*q*(Z/E)^2

n = 0.35*0.65*(1.6449/0.04)^2

n = 384.7162

Required sample size = n = 385