Voters

In this application exercise, we’ll do inference on a single population proportion.

Packages

We’ll use the tidyverse and tidymodels packages.

library(tidyverse)
library(tidymodels)

Data

In a survey conducted by Survey USA between September 30, 2023 and October 3, 2023, 2759 registered voters from all 50 US states were asked

America will hold an election for President of the United States next November. Not everyone makes the time to vote in every election. Which best describes you? Are you certain to vote? Will you probably vote? Are the chances you will vote about 50/50? Or will you probably not vote?

The data from this survey can be found in your data folder: voting-survey.csv.

Exercise 1

What, if anything, do you know about voter turnout in the US?

Add response here.

Exercise 2

Load the data and visualize the distribution of responses. Also calculate the proportion of respondents who are certain to vote in the next presidential election.

# add code here

Estimation

Based on these data, we want to estimate the true proportion of registered US voters who are certain to vote in the next presidential election.

Exercise 3

What is the parameter of interest?

Add response here.

Exercise 4

Estimate using a 95% bootstrap interval.

# add code here

Exercise 5

Suppose the bounds of this interval are L and U, your friend interprets the interval as

95% of the time, the true proportion of proportion of registered US voters who are certain to vote in the next presidential election is between L and U.

Comment on this interpretation. Is it correct? If not, how would ix it?

Add response here.

Testing

A newspaper claims that more than 60% of registered US are certain to vote in the next presidential election and cites this study as evidence. Do these data provide convincing evidence for this claim?

Exercise 6

What are the hypotheses?

Add response here.

Exercise 7

Conduct a randomization test, at 5% discernability level, for this claim. What is the conclusion of the test?

# add code here

Exercise 8

Suppose the p-value you found is P, and your friends are in disagreement about the interpretation about this value. One friend claims:

The probability that 60% of all of registered US voters are certain to vote in the next presidential election is P.

Another friend claims:

The probability that more than 60% of all of registered US voters are certain to vote in the next presidential election is P.

Who is right? Explain your reasoning.

Add response here.

Conceptual

Exercise 9

What is \(p\) vs. \(\hat{p}\) vs. p-value. Explain generically as well as in the context of these data and research question.

Add response here.

Exercise 10

What is sampling distribution vs. bootstrap distribution vs. null distribution? Explain generically as well as in the context of these data and research question.

Add response here.