Question

translate the statement into a confidence interval. approximate the level of confidence.
in a survey of 1015 parents of children ages 8 - 14, 63% say they are willing to get a second or part - time job to pay for their childrens college education and 36% say they lose sleep worrying about college costs. the surveys margin of error is ±3%.
use the results from the survey about getting a second or part - time job.
the confidence interval for the proportion is (□,□).
(round to three decimal places as needed.)

Explanation:

Step1: Calculate the lower bound

The formula for the lower bound of a confidence interval for a proportion is $\hat{p}-E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error.
Given $\hat{p} = 0.63$ and $E=0.03$, the lower bound is $0.63 - 0.03=0.60$.

Step2: Calculate the upper bound

The formula for the upper bound of a confidence interval for a proportion is $\hat{p}+E$.
Using $\hat{p} = 0.63$ and $E = 0.03$, the upper bound is $0.63+0.03 = 0.66$.

Answer:

$(0.600,0.660)$