Question

A researcher wishes to estimate the proportion of adults who have high-speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.01 with 90% confidence if :

(a) she uses a previous estimate of 0.42?
(b) she does not use any prior estimates?

Answer 1

How did you decide o use 0.5?

Answer 2

Part A:

n=6591.87≅6592

Part B:

n=6765.06≅6765

Explanation:

In order to calculate the sample size we use the following estimated Sample proportion formula:

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

Where:

p is the previous estimate

q is the 1-p

Z is the distribution

E is the margin

At 90% Confidence significance level is 0.1/2=0.05

Z at 0.05 or 5% =1.645

Part A:

p=0.42

q=1-p=1-0.42=0.58

Z=1.645

E=0.01

`n=0.42*0.58*(1.645^2)/(0.01^2)`

n=6591.87≅6592

Part B:

Since no prior estimate is given we assume p =0.5 and q=0.5

`n=0.5*0.5*(1.645^2)/(0.01^2)`

n=6765.06≅6765