Final answer:
The Gallup group accurately predicted the 1936 presidential election by using more sophisticated statistical methods and ensuring their sample was random and representative, unlike the Literary Digest, which had a biased sample.
Step-by-step explanation:
The Gallup group predicted the 1936 presidential election accurately because Gallup employed more sophisticated statistical methods and did not have a biased sample, unlike the Literary Digest poll. The Digest sent opinion cards to a non-random group of people - those with subscriptions, phone, or car registrations, leading to a skewed and non-representative sample. In contrast, Gallup's methods were more scientifically rigorous, utilizing a random sample that better represented the general population.
Moreover, the accuracy of a poll depends not solely on the sample size but also on the representativeness of the sample. While a larger sample size can reduce the margin of error, it's the randomness and representativeness of the sample that primarily determine the accuracy of the poll's predictions.