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 0.02 with a 90% confidence if
(a) she uses a previous estimate of 0.52
(b) she does not use any prior estimates?

(a) n=
(b) n=
round to the nearest integer

Answer 1

Solution :

Given that,

= 0.52

1 - = 1 - 0.52 = 0.48

margin of error = E = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 / 0.02)² * 0.52 * 0.48

=1688.6

Sample size = 1689

b

Solution :

Given that,

= 0.5

1 - =0.5

margin of error = E = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645} ( Using z table )

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 / 0.02)² * 0.5 * 0.5

=1691.265

Sample size = 1691 rounded