Participants in a survey were asked whether they favored or opposed the death penalty for people convicted of murder. Software shows the results below.
x
n
Sample p
95.0% CI
1764
2565
?
(0.670, 0.706)
Here, X refers to the number of respondents who were in favor.
(a) Show how to obtain the value that should be reported under "Sample p."
Sample p = X/n = 1764/2565 = 0.687 (3 decimal places)
(b) What is the margin of error for this confidence interval?
The margin of error can be calculated by subtracting the lower bound of the confidence interval from the upper bound and dividing it by 2.
Margin of error = (0.706 - 0.670)/2 = 0.018 (3 decimal places)
(e) Can you conclude that more than half of all American adults were in favor? Why?
No. All of the values in this interval are above 0.50. Yes. 0.50 is in this interval. No. 0.50 is not in this interval. Yes. All of the values in this interval are above 0.50.