Question

Race relations: A New York Times/CBS poll surveyed 1,027 adults nationwide about race relations in the United States. Of the sample, 61% 10 points responded that race relations in this country are generally bad. The 95% confidence interval is (0.58, 0.64). Which of the following is an appropriate interpretation of the 95% confidence interval?

A. There is a 95% probability that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.
B. We are 95% confident that the proportion of the sample who say that race relations in this country are generally bad is between 58% and 64%.
C. Of the samples, 95% will have between 58% and 64% of respondents who say that race relations in this country are generally bad.
D. We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.

Answer 1

D. We are 95% confident that the proportion of all Americans who say that race relations in this country are generally bad is between 58% and 64%.

Explanation:

The 95% confidence interval refers that 95% of data is correct with respect of the population

Given that 95% confidence interval is (0.58, 0.64)

So based on this, the option D is correct as it shows the right thing with regard to 95% confidence interval

Therefore all the other options are incorrect as the first option is of probability, the second option is the sample, and the third option is of statement form i.e not standardized.