Question

A survey was conducted with randomly selected 1012 California residents of age 18

and older. One of the questions on the survey was, “Are you in favor of death

penalty for a person convicted of murder?” 693 of the surveyed answered yes.

Check the conditions and construct 90% confidence interval for proportion of

California residents age 18 or older who are in favor of death penalty. (Find

critical value, margin of error, confidence interval, and state the conclusion)

Answer 1

sample proportion = 693 / 1012 = 0.685

n = 0.685 * 1012 = 693 > 10

n ( 1 - ) = 1012 * ( 1 - 0.685) = 319 > 10

Since n > 10 and n ( 1 - ) > 10 ,

Sampling distribution of proportin is approximately normal.

Margin of error = Z/2 * sqrt [ ( 1 - ) / n ]

= 1.645 * sqrt [ 0.685 * ( 1- 0.685) / 1012 ]

= 0.024

90% CI is

- E < P < + E

0.685 - 0.024 < p < 0.685 + 0.024

0.661 < p < 0.709

90% CI is ( 0.661 , 0.709 )