Question

The Pew Research Group conducted a poll in which they asked, "Are you in favor of, or opposed to, executing persons as a general policy when a capital crime is committed while under the age of 18?" Of the 580 Catholics surveyed, 163 indicated they favored capital punishment; of the 600 seculars (those who do not associate with a religion) surveyed, 221 favored capital punishment. Construct a 95% confidence interval for the difference in the proportion p1 of Catholics who favor the death penalty in such situations, and the proportion p2 of seculars who favor the death penalty. (Use sample proportions rounded to 3 decimal places in the following calculations.)

Conditions: n subscript 1 p with hat on top subscript 1 open parentheses 1 minus p with hat on top subscript 1 close parentheses equals (Round to 3 decimal places.) n subscript 2 p with hat on top subscript 2 open parentheses 1 minus p with hat on top subscript 2 close parentheses equals (Round to 3 decimal places.)

Confidence Interval: We are 95% confident that the proportion of Catholics who favor the death penalty for capital crimes committed under the age of 18 is between (lower) and (upper) (less / greater) than the corresponding proportion of seculars. (Round to 3 decimal places. Remember to report absolute values of the bounds. If both bounds have the same sign, report the smaller absolute value first (lower).

Use the confidence interval found in Question 5 to test the hypotheses

H₀: p₁-p₂ = 0
H_a: p₁-p₂ ≠ 0

Since 0 is  (inside / outside) the confidence interval, the data  (does / does not) provide significant evidence that the proportion of Catholics who favor the death penalty for capital crimes committed while under the age of 18 differs from the corresponding proportion of seculars.

Answer 1

n₁(1 - ) = 580*0.281*(1 - 0.281) = 117.191

n₂(1 - ) = 600*0.3254*(1 - 0.3254) = 139.598

We are 95% confident that the proportion of Catholics who favor the death penalty for capital crimes committed under the age of 18 is between -0.140 and -0.034 less than the corresponding proportion of seculars.

Since 0 is  outside the confidence interval, the data does  provide significant evidence that the proportion of Catholics who favor the death penalty for capital crimes committed while under the age of 18 differs from the corresponding proportion of seculars.

p1	p2	pc
0.281	0.3683	0.3254	p (as decimal)
163/580	221/600	384/1180	p (as fraction)
163.	221.	384.	X
580	600	1180	n
	-0.0873	difference
	0.	hypothesized difference
	0.0273	std. error
	-0.14	confidence interval 95.% lower
	-0.034	confidence interval 95.% upper
	0.0532	margin of error