Question

A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United States citizens. The citizens in each sample were asked whether they were optimistic about the economy. For each sample, the polling agency created a 95 percent confidence interval for the proportion of all United States citizens who were optimistic about the economy. Which of the following statements is the best interpretation 5. A e 95 percent confidence level? (A) with 100 confidence intervals, we can be95% co nfident that the sample proportion of citizens of the (B) We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the (C) We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of (D) Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from (E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sample United States who are optimistic about the economy

Answer 1

We would expect about 95 of the 100 confidence intervals to contain the proportion of all citizens of the United States who are optimistic about the economy.

Explanation:

Answer 2

Correct option (B).

Explanation:

A 95% confidence interval for a population parameter implies that there is 0.95 probability that the population parameter is contained in that interval.

Or, if 100, 95% confidence intervals are created then 95 of those intervals would contain the population parameter with probability 0.95.

In this question the 95% confidence interval was created for population proportion of all United States citizens who were optimistic about the economy.

Then this 95% confidence interval implies that if 100 such confidence intervals were created then 95 of those would consist of the true proportion of US citizens who were optimistic about the economy..

Thus, the correct option is (B).