Question

A planning board in Elm County is interested in estimating the proportion of its residents that are in favor of offering incentives to high-tech industries to build plants in that county. A random sample of Elm County residents was selected. All of the selected residents were asked, "Are you in favor of offering incentives to high-tech industries to build plants in your county?" A 95 percent confidence interval for the proportion of residents in favor of offering incentives was calculated to be 0.54 ± 0.05. Which of the following statements is correct? (As an added challenge: Can you find the mistakes in the incorrect statements?)
a) At the 95% confidence level, the estimate of 0.54 is within 0.05 of the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county.
b) At the 95% confidence level, the majority of area residents are in favor of offering incentives to high-tech industries to build plants in the county.
c) In repeated sampling, 95% of the sample proportions will fall in the interval (0.49, 0.59).
d) In repeated sampling, the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county will fall in the interval (0.49, 0.59).
e) In repeated sampling, 95% of the time the true proportion of county residents in favor of offering incentives to high-tech industries to build plants in the county will be equal to 0.54.

Answer 1

Answer:

Given confidence interval is 0.54+or-0.05

0.54-0.05,0.54+0.05 =

(0.49,0.59)

In repeated sampling,the true proportion of country residents in favor of offering incentives to high-tech industries to build plants in the country will fall in the interval (0.49,0.59)