1. Think about the elevator study that I had you read about for the first class. Imagine that I want to design a similar study for the 2024 reelection campaign of Josh Dobson (assuming he runs) to see if his pictures have a similar effect as did Cherie Berry’s pictures. However, I don’t want to wait three years to do the study so I want to do an experiment. Discuss how you might suggest that I go about doing that. In this answer, please present a null and alternative hypothesis and discuss the four principles of experimental design. Please also discuss blinding, the importance of confounding variables, and whether you could infer causality from the experiment. Please write in paragraph form (but you can list hypotheses if you prefer for that section). (10 pts.)
2. On June 23, 2016, the referendum to pass the European Union shockingly passed in the United Kingdom. In this problem, you are going to be working with data from that election. The below charts from Wikipedia shows support for the referendum by age and education level. I’ve provided the chart both in color and greyscale. (24 pts.)
a. What relationship does age seem to have with support for Brexit? What relationship does education seem to have with support for Brexit? (“GCSE or lower” is the group with the least educational attainment, while “Degree” has the most.) Do these values always increase or decrease? Do we know the percentage of the total electorate in each group and if not, how might we change the visualization to learn this? (10 pts.)
3. Two weeks ago, California Governor Gavin Newsom faced a recall vote. California has an odd recall system whereby voters first decide whether to vote “yes” or “no” on the recall and then (regardless of how they voted in the first round) vote for a candidate who will take the governorship if the recall passes. While Arnold Schwarzenegger won the most votes in Round 2 in 2002, Democrats tried to hold the governorship by encouraging a vote for Democratic Lieutenant Governor Cruz Bustamante, who used the slogan “No on Recall, Yes on Bustamante” to encourage voters to oppose the recall, but the vote for him. (10 pts.)
a. The recall failed in 15 of California’s 58 counties and Bustamante won 9 counties. Given that a county voted “No” on the Recall, there is a 60% chance that it voted “Yes on Bustamante.” What is the probability that a county voted against the recall given that it voted for Bustamante? Please use Bayes’ Rule and show your work. (5 pts.)
b. In his 2006 reelection bid against Democratic California State Treasurer Phil Angelides, Arnold Schwarzenegger won 52 of California’s 58 counties and Angelides the other 6. Given that a county voted for Angelides, there is an 83.33% chance it voted for Bustamante three years earlier (i.e., 5 counties). What is the probability that a county voted for Angelides given that it had voted for Bustamante? Please use Bayes’ Rule and show your work. (5 pts.)
4. In the 14 public polls released after September 1st of last year, Senator Susan Collins (R-ME) trailed Democratic State House Speaker Sara Gideon in each of these polls which had an average of 750 likely voters. Yet on election night, Collins pulled off a surprise reelection win with 51 percent of the vote. Imagine that a pollster decided to conduct a series of polls of sample size 750 of this special election right before it took place using random sampling. What would µp̂ and SEp̂ be equal to here? (Please calculate these.) What percent of the time would you expect these polls to either show a tie or show Collins ahead? Is it surprising that Collins did not lead any of the actual polls that were taken? Would you suggest pollsters investigate what might have gone wrong with their sampling? Please show all work and explain how you got your answers for each part of this problem. (15 points)
5. The pollster Rasmussen Reports (we’ll discuss them more after the exam) tweeted out the below tweet quoting an article from the Washington Times. (20 pts.)
a. Rasmussen polled 1,000 likely voters for this poll. Is the above tweet correct? Using this information and the information above, please assess this claim. (10 pts.)
b. The article attached to the above tweet notes that “Republican state Sen. Peggy Lehner said Mr. Trump has lost support in her suburban Dayton district in western Ohio.” Ohio has 33 state Senate districts of approximately the same population. Assuming the poll sampled equally from all state Senate districts, what would the margin of error be for a candidate at 50% of the vote for the subgroup of those in Lehner’s district? What might you do differently if you were especially interested in providing a precise estimate of the support for Trump in Lehner’s district? Please show all of your work. (10 pts.)