Question

A random sample of individuals participating in a survey in 2000 was asked ""Do you favor or oppose the death penalty for murder?"" The results were 130 out of 200 females favored capital punishment and 188 out of 250 males favored capital punishment. Find an approximate 95% confidence interval for the difference between the proportion of females and males that favor capital punishment. Based upon your confidence interval do you believe the proportion of males that favor capital punishment is greater than the proportion of females that favor capital punishment? Justify your answer.

Answer 1

At 5% significance level, the two proportions are equal.

Explanation:

Given that a random sample of individuals participating in a survey in 2000 was asked ""Do you favor or oppose the death penalty for murder?""

Label:

Females Males Total

N 200 250 450

X 130 188 318

p 0.7222 0.752 0.7067

`H_0: p_f = p_m\\H_a: p_f <p_m`

(left tailed test)

p difference = -0.0298

Standard error for difference =
`\sqrt{(0.7067*0.2933)/(450) } \\=0.0215`

Z statistic =
`(-0.0298)/(0.0215) \\=-1.386`

p value = 0.0828

Since p >0.05, we accept H0

At 5% significance level, the two proportions are equal.