Q2 (10 points) In the 2020 US presidential election (Nov 3, 2022) Joe Biden received 51.3% of the popular vote while Donald Trump received 46.9%; the rest went to minor candidates. The wikipedia page at https://en.wikipedia.org/wiki/Nationwide_opinion_polling_for_the_2020_United_States_presidentia|_election lists the results of a large number of surveys of the 2020 US Presidential election. It has been widely suggested that the polls did a bad job of predicting the results of the election and this question is about one sort of evidence about whether that criticism is fair. I count (on 2022/01/07) 184 rows in the table. | used the column labelled Date to sort the polls so that the most recent poll end dates were at the top. Attached to this question is a screen shot of the first 29 rows when the table is sorted in this order. These are all the polls whose end date was October 31 or later. These are the 29 rows I want you to use to answer the following questions: \fa) What fraction of these polls overestimated the percentage of the vote Biden would receive? Answer the same question for Trump. b) What number of these polls gave a margin of error? 0) What number of these polls gave a margin of error bigger than the difference between their prediction of the Biden share and the actual figure of 51.3%? [It is not easy to decide in every case if a poll result is less than what Biden actually got or more; do your best and explain how you counted] Also give the same number for Trump compared to his actual share of 46.9%. d) Express the answers to c as a percentage of the answer to b. e) Discuss in a couple of sentences whether the numbers above suggest that the polling 'failed'. f) Read a few of the footnotes and describe some problems with the way I have asked this