Question

A zoning board in Pine County is interested in estimating the proportion of its residents in favor of larger school zones in that county. A random sample of Pine County residents was selected. All the selected residents were asked, "Are you in favor of larger school zones in your county?" A 95% confidence interval for the proportion of residents in favor of larger school zones in that county was calculated to be 0.48 ± 0.02. Which of the following statements is correct?

A) At the 95% confidence level, the majority of area residents is in favor of larger school zones in that county.
B) In repeated sampling, 95% of sample proportions will fall in the interval (0.46, 0.50).
C) At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.
D)In repeated sampling, the true proportion of county residents in favor of larger school zones in that county will fall in the interval (0.46, 0.50).
E) In repeated sampling, 95% of the time, the true proportion of county residents in favor of larger school zones in that county will be equal to 0.48.

Answer 1

C) At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.

Explanation:

x% confidence interval:

A confidence interval is built from a sample, has bounds a and b, and has a confidence level of x%. It means that we are x% confident that the population mean is between a and b.

In this question:

95% CI between 0.48 - 0.02 = 0.46 and 0.48+0.02 = 0.5.

The interpretation is that we are 95% sure that the true population proportion is in this interval, that is, with 95% confidence, the estimate is within 0.02 of the true proportion, and so the correct answer is given by option C.