Final answer:
The margin of error for the given confidence interval (0.512 < p < 0.849) is 0.1685, which is calculated based on the midpoint of the interval.
Step-by-step explanation:
To determine the margin of error for the confidence interval for the proportion, we look at the formula for a confidence interval which is (p' - EBP, p' + EBP), where EBP represents the error bound for the proportion. Given a confidence interval of 0.512 < p < 0.849, we can calculate the margin of error by finding the distance between the point estimate p' and one of the boundaries of the interval.
The point estimate p' would be the midpoint of the interval. We calculate it as the average of the lower and upper bounds: p' = (0.512 + 0.849) / 2
= 0.6805. To find the margin of error, we subtract the point estimate from the upper bound or vice versa with the lower bound:
EBP = 0.849 - 0.6805
= 0.1685 (or alternatively EBP = 0.6805 - 0.512)
The margin of error is 0.1685, which indicates the extent of the interval around the point estimate that we expect to contain the true population proportion with a certain level of confidence.