Question

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 90​% confidence if

​(a) he uses a previous estimate of 32%?

​(b) he does not use any prior​ estimates?

​(a) n=_____

​(Round up to the nearest​ integer.)

​(b) n=______

​(Round up to the nearest​ integer.)

Answer 1

Solution :

Given that,

= 0.32

1 - = 1 - 0.32= 0.68

margin of error = E = 2% = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.02)2 * 0.32 * 0.68

=1472.07

Sample size = 1472

B)

Solution :

Given that,

= 0.5

1 - = 1 - 0.5= 0.5

margin of error = E = 2% = 0.02

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= (1.645 / 0.02)2 * 0.5 * 0.5

=1691.26

Sample size = 1692