Question

checkpoint question: adding and subtracting our margin of error of $me = 0.0402$ to our point estimate of $hat{p}=0.48$ gets us our 99% confidence interval of $0.48pm0.0402$ or $(.4398, .5202)$. interpret this confidence interval for $p =$ the true proportion of u.s. adults who \often or always\ got enough sleep during the past 7 nights in context. type your answer below and be specific! type your answer here

Explanation:

A confidence interval gives a range of values within which the true population parameter (here, the proportion \(p\) of U.S. adults who "often or always" got enough sleep in the past 7 nights) is likely to lie. The 99% confidence level means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population proportion \(p\).

In this case, the interval \((0.4398, 0.5202)\) was calculated using the point estimate \(\hat{p}=0.48\) and margin of error \(ME = 0.0402\).

Answer:

We are 99% confident that the true proportion \(p\) of U.S. adults who “often or always” got enough sleep during the past 7 nights is between \(0.4398\) and \(0.5202\). This means that if we were to repeat the sampling process many times and construct 99% confidence intervals each time, approximately 99% of those intervals would capture the actual value of the proportion \(p\) in the entire population of U.S. adults.