Question

A researcher wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes to estimate to be within 4 percentage points with 98% confidence if

a) he uses a 2006 estimate of 14% obtained from another poll?

b) he does not use any prior estimate?

Answer 1

Solution :

Given that,

= 0.14

1 - = 1 - 0.14 = 0.86

margin of error = E = 4% = 0.04

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

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

= (2.326 / 0.04)2 * 0.14 * 0.86

=407.12

Sample size = 407

b

Solution :

Given that,

= 0.5

1 - = 1 - 0.5 = 0.5

margin of error = E = 4% = 0.04

At 98% confidence level the z is,

= 1 - 98%

= 1 - 0.98 = 0.02

/2 = 0.01

Z/2 = 2.326 ( Using z table )

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

= (2.326 / 0.04)2 * 0.5 * 0.5

=845.355

Sample size = 845