Recall from Exploration 3.5A that the Literary Digest magazine conducted a very extensive public opinion poll in 1936 in order to predict the outcome of that year’s presidential election. They mailed out over 10 million questionnaires to people whose names and addresses they obtained from telephone books and vehicle registration lists. They received more than 2.4 million responses, with 57% of the responses indicating an intention to vote for Republican challenger Alf Landon over the Democratic incumbent Franklin Roosevelt.
a. Use the Theory-Based Inference applet to produce a 99.9% confidence interval. Also interpret this interval.
b. Why is this interval so narrow, even with an extremely large confidence level of 99.9%?
c. Would you really have a lot of confidence that this interval succeeds in capturing the population proportion of American voters who intended to vote for Landon in 1936? Why or why not?