Question

Let p equal the proportion of Americans who favor the death penalty. If a random sample of n = 1234 Americans yielded y = 864 who favored the death penalty, find an approximate 95% confidence interval for p.

Answer 1

(0.6744,0.7258)

Explanation:

Given that p equal the proportion of Americans who favor the death penalty.

`n=1234\\y=864\\p=(864)/(1234) \\=0.7002\\q=0.2998`

std error =
`\sqrt{(pq)/(n) } \\=0.0130`

95% confidence interval=p±*margin of error

margin of error = 1.96*std error =0.0256

Confidence interval lower bound=
`0.7002-0.0256\\=0.6744`

Upper bound =
`0.7002+0.0256\\=0.7258`

(0.6744,0.7258)