Question

Excluding voters for third‑party candidates, approximately 52% of the voters in Virginia's 2012 presidential election voted for Barack Obama, with the other 48% voting for Mitt Romney. In modern presidential politics, the vote in Virginia this year was not particularly close. Obama fairly easily won more than 50% of the votes, claiming Virginia's 13 electoral college votes.

Use the Statistical Applet: Confidence Intervals for Proportions to simulate what might have happened in 25 pre‑election polls, with each poll including a sample size of 250 people. Click RESET. Set ? to 0.52 and ?n to 250. Click SAMPLE 25.

Inspect the 95% confidence intervals of these 25 simulated polls. How many of them include the true population proportion of 0.52?

Answer 1

All of them (25 out of 25 polls) include the true population proportion of 0.52 which is shown below:

Let's Reset and click on SAMPLE 25 again with p =0.52 and n =250. This time 23 out of 25 polls include the true population proportion of 0.52 as shown below:

Red bars indicate that they do not include 0.52

You can repeat this process of resetting and clicking on SAMPLE 25 by keeping p =0.52 and n =250.