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 0.04 with 95 % confidence:

a) assuming a previous study concluded that the proportion of adults who have high-speed internet access was 0.48?

b) assuming the researcher has no previous results to reference?

Answer 1

Solution :

Given that,

margin of error = E = 0.04

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

(a)

= 0.48

1 - = 1 - 0.48 = 0.52  

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.04)² * 0.48 * 0.52

= 599.28 = 600

sample size = 600

(b)

= 0.5

1 - = 1 - 0.5 = 0.6

sample size = n = (Z _{/ 2} / E )² * * (1 - )

= (1.96 / 0.04)² * 0.5 * 0.5

= 600.25

sample size = 601