Case Study: Polls

Let’s now switch gears to a more realistic sampling scenario than our bowl activity—a poll. In practice, pollsters don’t take 1,000 repeated samples, but rather take only a single sample that’s as large as possible.

On December 4, 2013, National Public Radio in the US reported on a poll of President Obama’s approval rating among young US citizens aged 18–29 in an article, “Poll: Support For Obama Among Young Americans Eroding.” A quote from the article stated:

“After voting for him in large numbers in 2008 and 2012, young Americans are souring on President Obama. According to a new Harvard University Institute of Politics poll, just 41 percent of millennials—adults aged 18–29—approve of Obama’s job performance, his lowest-ever standing among the group and an 11-point drop from April.”

Let’s tie elements of the real-life poll in this new article with our tactile and virtual bowl activity using the terminology, notations, and definitions we learned previously. We’ll see that our sampling activity with the bowl is an idealized version of what pollsters are trying to do in real life.

First, who is the (study) population of $N$ individuals or observations of interest?

• Bowl:$𝑁$= 2,400 identically sized red and white balls

• Obama poll:$𝑁$= ? young US citizens aged 18–29

Second, what’s the population parameter?

• Bowl: The population proportion $p$ of all the balls in the bowl that are red

• Obama poll: The population proportion $p$ of all young US citizens who approve of Obama’s job performance

Third, what would a census look like?

• Bowl: Manually going over all $N$ = 2400 ...