A polling agency conducted a survey by selecting 100 random samples, each consisting of 1,200 United Statescitizens. 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 wereoptimistic about the economy. Which of the following statements is the best interpretation of the 95 percentconfidence level?(A) With 100 confidence intervals, we can be 95% confident that the sample proportion of citizens of the UnitedStates 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 theUnited 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 ofthe 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 fromsamples of the same size of 1,200.(E) The probability is 0.95 that 100 confidence intervals will yield the same information about the sampleproportion of citizens of the United States who are optimistic about the economy.
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
proportion of citizens of the United States who are optimistic about the economy.
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