Question

Consider the following data collected in two recent surveys of whether voters in cities A and B favor a ballot proposition in the next election. City Sample Size In Favor A 615 463 B 585 403 Suppose you're going to find a confidence interval for the difference between the population proportions in the two cities. What's the standard error of the estimate of the difference between the two proportions?

Answer 1

Standard error of the estimate of the difference between the two proportions=0.0259

Explanation:

Given that the following data collected in two recent surveys of whether voters in cities A and B favor a ballot proposition in the next election.

City A B Total

Sample size 615 585 1200

Favour X 463 403 866

Proportion p 0.7528 0.6889 0.7217

Std error for difference

=
`\sqrt{p(1-p)((1)/(n_1) }+ (1)/(n_2) \\`

p =0.7217

1-p = 0.2783

by substituting p and n1 = 615 and n2 = 585 we get

Std error = 0.0259

Standard error of the estimate of the difference between the two proportions=0.0259