In: Statistics and Probability
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 99% confidence if
(a) she uses a previous estimate of 0.28?
(b) she does not use any prior estimates?
Solution :
Given that,
= 0.28
1 - = 1 - 0.28 = 0.72
margin of error = E = 0.04
At 99% confidence level the z is,
= 1 - 99%
= 1 - 0.99 = 0.01
/2 = 0.005
Z/2 = 2.58 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (2.58 / 0.04)2 * 0.28 * 0.72
=839
Sample size = 839
B
Given that,
=0.5
1 - = 0.5
margin of error = E = 0.04
At 99% confidence level the z is,
= 1 - 99%
= 1 - 0.99 = 0.01
/2 = 0.005
Z/2 = 2.58 ( Using z table )
Sample size = n = (Z/2 / E)2 * * (1 - )
= (2.58 / 0.04)2 * 0.5 * 0.5
=1040
Sample size = 1040