Question

Question text

In a random sample of 200 people, 32 people have blue eyes (characteristic B). Which of the following 95% confidence intervals estimate the true proportion pp of measurements in the population with characteristic B?

Select one:

a. (0.109, 0.211)

c. (0.431, 0.712)

d. (0.561, 0.912)

Answer 1

Solution :

Given that,

n = 200

x = 32

Point estimate = sample proportion = = x / n = 32 / 200 = 0.160

1 - = 1 - 0.160 = 0.840

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.160 * 0.840) / 200)

= 0.051

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.160 - 0.051 < p < 0.160 + 0.051

0.109 < p < 0.211

(0.109 , 0.211)

Option a)