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 of the 95 percent confidence level?
A. With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the United States who are optimistic about the economy is correct.B. 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.C. We would expect about 5 of the 100 confidence intervals to not contain the sample proportion of citizens of the United States who are optimistic about the economy.D. Of the 100 confidence intervals, 95 of the intervals will be identical because they were constructed from samples of the same size of 1,200.E. The probability is 0.95 that 100 confidence intervals will yield the same information about the sample proportion of citizens of the United States who are optimistic about the economy

Answer 1

Answer:

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.

Step-by-step explanation:

The purpose of sampling is to make statistical inference the entire population of interest. Thus, we generalized to the entire population the findings from the sample.

For instance, we don't need to drink entire cup of coffee to know whether the sugar is enough or not. We only need to stir (randomly) and take a sip from the cup of coffee. We usually assume that, if the content we sipped is satisfactory to our taste, the entire content of coffee inside the cup is satisfactory. Using this illustration, we would expect that the findings of the survey should be generalized to the entire population of study.

Thus, 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.