Question

A sample of n = 1,033 adults in the United States was asked, "Do you think the police should or should not be allowed to collect DNA information from suspected criminals, similar to how they take fingerprints?" Of those sampled, 68% answered "should". (Round your answers to the nearest tenth.)

(a) Calculate the conservative margin of error for the survey, as a percentage.

(b) Compute an approximate 95% confidence interval for the percentage of all American adults who think police should be allowed to collect DNA information from suspected criminals.

Answer 1

Solution :

Given that,

n = 1033

Point estimate = sample proportion = = 0.68

1 - = 1 - 0.68 = 0.32

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025 = 1.960

a) Margin of error = E = Z / 2 * (( * (1 - )) / n)

Margin of error = E = 1.96 (((0.68 * 0.32) / 1033 )

  Margin of error = E = 0.028

Margin of error = E = 2.8%

b) A 95% confidence interval for population proportion p is ,

± E

= 0.68 ± 0.028

=( 0.652, 0.708 )

= ( 65.2%, 70.8% )