Question

Determine the margin of error for a 99​% confidence interval to estimate the population proportion with a sample proportion equal to 0.80 for the following sample sizes.

a. n=100             b. n=200             c. n=260

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.80

Z_/2 = 2.576

(a) n = 100

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.80 * 0.20) / 100)

= 0.103

(b)

n = 200

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.80 * 0.20) / 200)

= 0.073

(c)

n = 260

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.80 * 0.20) / 260)

= 0.064