Question Set 1. Estimating the Proportion of Voters

The following questions are related to the proportion of registered voters who said they were

planning to vote for "Candidate A" in the next city council election.

A. In a representative sample of 30 voters, 18 said they were planning to vote for Candidate A.

Use StatKey to construct a 95% bootstrap confidence interval using the percentile method to

estimate the proportion of all registered voters in the population who are planning to vote for

Candidate A. You can enter the sample data into StatKey using the "Edit Data" button.

Remember to take at least 5,000 resamples. Don't forget to include a screenshot from StatKey

and to clearly identify your answer. [14 points]

B. Interpret the meaning of the confidence interval constructed in part A by completing the

phrase below. [5 points]

I am 95% confident that...

C. Given your confidence interval in part A, is there evidence that the proportion of all

registered voters in the population who are planning to vote for Candidate A is different from

0.50 (i.e., half)? Explain why or why not. [5 points]

D. What if the sample size were 10 times bigger? Find the confidence interval if we had a

sample where 180 out of 300 participants were planning to vote for Candidate A. Use StatKey

to construct a 95% confidence interval using the percentile method with these new data

(x=180, n=300). Take at least 5,000 resamples. Don't forget to include a screenshot from

StatKey and to clearly identify your answer. [14 points]

E. When the sample size was increased, how did the confidence interval change? Explain why.

[5 points]

F. Using the dataset with 180 out of 300 participants planning to vote for Candidate A,

construct a 99% confidence interval in StatKey using the percentile method. Take at least

STAT 200 Lesson 4: Confidence Intervals

Due Tuesday, June 15, 2021

5,000 resamples. Don't forget to include a screenshot from StatKey and to clearly identify your

answer. [14 points]

G. When the confidence level was changed from 95% to 99%, how did the confidence interval

change? Explain why. [5 points]

Question Set 2. Estimating the Difference in Mean Commute Distances

For the following questions, you will use StatKey to construct bootstrap confidence intervals for the

difference in two means. Use the "Commute Distance (Atlanta - St. Louis)" dataset built into StatKey.

A. Using the percentile method, construct a 95% confidence interval for the difference in the

mean commute distances in Atlanta and St. Louis. Take at least 5,000 resamples. Don't forget

to include a screenshot from StatKey and to clearly identify your answer. [14 points]

B. Describe the shape of your bootstrap distribution from part A. Is it normally distributed or

skewed? [5 points]

C. Using the standard error method, construct a 95% confidence interval for the difference in

the mean commute distances in Atlanta and St. Louis. You can use the standard error from the

bootstrap distribution you constructed in part A. Show all of your work using the equation

editor. [14 points]

D. Explain why the confidence intervals you constructed using the percentile method and the

standard error method are not exactly the same. In other words, why may we expect answers

in parts A and C to be slightly different? [5 points