In Example 2.1, you saw that the percentage of people who said they voted in the 2016 presidential election from the General Social Survey (GSS) (69.8%) was significantly different than the percentage of people that actually voted in that election (59.2%). You also saw that this difference came from a nonsampling concern. Some people are not honest when they are answering a question the answer to which can be perceived as undesirable—like saying they did not vote. Let’s take another look at that example. From the GSS, we saw that 1,523 said they voted out of 2,181 people that were eligible to vote and answered yes or no to the question of whether or not they voted. Thirty-five people were asked this question and either did not respond or said that they could not remember whether they voted. Let’s add these people to the total number that were asked the question. So our new proportion is 1,523 said they voted out of 2,216 eligible voters that were asked the question. 

a. Is the new proportion (1,523/2,216) closer to the actual proportion that voted than what you saw in the example? 

b. What is the standard deviation of sample proportions when you take samples of 2,216 from the population of all eligible voters, where the proportion that voted in the population is 0.592? 

c. How many standard deviations is the sample proportion of 1,523/2,216 above 0.592? Is the General Social Survey (GSS) result still significantly larger than the actual result? Explain.

Data from Example 2.1

In 2018, the General Social Survey (GSS) asked more than 2,300 adult Americans the following question: In 2016, you remember that Clinton ran for president on the Democratic ticket against Trump for the Republicans. Do you remember for sure whether or not you voted in that election? Of the 2,181 respondents who were eligible to vote and remembered whether they had voted, 1,523 (69.8%) said they voted  We would like to use these results to estimate the proportion of all eligible voters that voted: the parameter of interest. But, if we refer to the United States Election Project (http://www. electproject.org/), it reports that 136,753,936 ballots were cast for president that year, with 230,931,921 citizens eligible to vote, corresponding to 59.2% voter turnout, which is quite different from our sample statistic of 69.8%.