Question

From a SRS of 1000 registered voters in the U.S., 75% said that they planned to vote in the next national election. Find a 95% confidence interval estimate for the population proportion of registered voters in the United States who plan to vote in the next general election.

a)     Find the margin of error

b)    Construct the endpoints of the interval

c)     Write the interval

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.75

1 - = 1 - 0.75 = 0.25

  Z/2 = Z0.025 = 1.96

a) Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.96 (((0.75 * 0.25) / 1000)

= 0.013

A 95% confidence interval for population proportion p is ,

± E

0.75  ± 0.013

(0.737 , 0.763)

A. One can be 90% confident that thepopulation proportion of registered voters in the United States who plan to vote in the next general election is between 0.737 and 0.763