A survey asked whether respondents favored or opposed the death penalty for people convicted of murder. Software shows the results below, where X refers to the number of the respondents who were in favor. Construct the 95% confidence interval for the proportion of the adults who were opposed to the death penalty from the confidence interval stated below for the proportion in favor. X N Sample p 95.0% CI
1786 2611 0.684 (0.666,0.702 )
The 95% confidence interval for those opposed is: (.666 . 666, .702 . 702).

The 95% confidence interval for those opposed is: (0.298, 0.334).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

1786 of the 2611 were in favor, so 2611 - 1786 = 825 were opposed. Then

95% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 95% confidence interval for those opposed is: (0.298, 0.334).

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)