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 90​% confidence if ​a) she uses a previous estimate of 0.28​? ​ b) she does not use any prior​ estimates? ​

a) nequals nothing ​(Round up to the nearest​ integer.)

​b) nequals nothing ​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

a) = 0.28

1 - = 1 - 0.28 = 0.72

margin of error = E = 0.02

  At 90% confidence level the z is,

= 1 - 90%

= 1 - 0.90 = 0.10

/2  = 0.05

Z_/2 = Z _0.05 = 1.645

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

= (1.645 / 0.02 )² * 0.28 * 0.72

= 1363.83

sample size = n = 1364

b) = 1 - = 0.5

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

= ( 1.645 / 0.02 )² * 0.5 * 0.5

= 1691.26

sample size = n = 1692