Question

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for p is 0.28

(b) there is no preliminary estimate for p

Answer 1

Solution :

margin of error = E = 0.1

Z_/2 = 1.96

(a)

= 0.28

1 - = 0.72

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

= (1.96 / 0.1)² * 0.28 * 0.72

= 77.4

sample size = n = 78

(b)

= 0.5

1 - = 0.5

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

= (1.96 / 0.1)² * 0.5 * 0.5

= 96.04

sample size = n = 96