Question

College officials want to estimate the percentage of students who carry a gun, knife, or other such weapon. How many randomly selected students must be surveyed in order to be 97% confident that the sample percentage has a margin of error of 2 percentage points?

(a) Assume that there is no available information that could be used as an estimate of p^.

(b) Assume that another study indicated that 77% of college students carry weapons.

Answer 1

Solution :

Given that,

margin of error = E = 2% = 0.02

At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03 / 2 = 0.015

Z_/2 = Z_0.015 = 2.17

(a)

= 0.5

1 - = 1 - 0.5 = 0.5

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

= (2.17 / 0.02)² * 0.5 * 0.5

= 2943.06

sample size = 2944 students

(b)

= 0.77

1 - = 1 - 077 = 0.23

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

= (2.17 / 0.02)² * 0.77 * 0.23

= 2084.86 = 2085

sample size = 2085 students