A simple random sample of 450 residents in the state of New

A simple random sample of 450 residents in the state of New York is taken to estimate the proportion of people who live within 1 mile of a hazardous waste site. If a 95% confidence interval were calculated for a scenario where p = 0.3 and another scenario where p = 0.7, how would the two confidence intervals compare?

a. Since the sample proportion in the first scenario is smaller, its confidence interval would be narrower

b. Since the sample proportion in the second scenario is larger, its confidence interval would be shifted to the right and narrower than the one calculated from the first scenario.

c. Even though the sample proportions are different, the widths of the confidence intervals would be equal.

d. This cannot be determined from the information given.

Solution

c. Even though the sample proportions are different, the widths of the confidence intervals would be equal.

because standard error contains term sqrt(p-hat * (1-p-hat) / n)