Founded in 1890, the Literary Digest was a popular magazine in the early 1900s. The magazine correctly predicted the outcomes of the 1916, 1920, 1924, 1928, and 1932 presidential elections by conducting polls. With the Great Depression in full swing, the magazine ventured forth in 1936 to predict another presidential election outcome. Questionnaires were mailed out to more than 10 million adult Americans 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 for the proportion of all adult Americans who intended to vote for Alf Landon in 1936. Also interpret this interval. 

b. Why is your interval from part (a) so narrow, even with an extremely large confidence level of 99.9%? 

c. Alf Landon actually received 36.5% of the votes cast in the election. Does your 99.9% confidence interval include 0.365? Does it come close?

d. Do you think the Literary Digest‘s extremely misleading result can be blamed on selecting a nonrepresentative sample or on nonsampling concerns? Explain. 

e. An up-and-coming pollster named George Gallup made his first election prediction in 1936, the same year as the infamous Literary Digest poll. Gallup surveyed a random sample of 50,000 adult Americans and was able to predict the election result correctly. Do you think Gallup just got lucky or how do you suspect that he did better than Literary Digest? Explain.