Lesson 12 So, You Say There’s a Chance? Practice Understanding

Learning Focus

Use statistical reasoning to evaluate claims in the media.

How can we tell if the results of polls or other studies are being reported accurately?

Open Up the Math: Launch, Explore, Discuss

In 2018, Eric Reid shared a photo on Twitter of a note he received from the NFL: “You have been randomly selected by the NFL drug testing program’s Medical Advisor to complete a urine doping test today.” Below the note, he commented, “Number 7… ‘Random,’” indicating his belief that he was being unfairly selected for drug testing.

The NFL tests all players in the preseason for use of prohibited substances, and after that, each week the NFL randomly selects $10$ players from each team for drug testing. After the preseason, Eric Reid was selected for testing $6$ out of the next $11$ weeks.

As reported in an article in Sports Illustrated, “By noting the alleged frequency of the tests, Reid is clearly calling into question the ‘randomness’ of the league’s drug-testing system, at least as it relates to him. He and many NFL observers are dubious, and some believe more nefarious factors are afoot as they relate to the league and one of its most outspoken players—one who happens to be suing the league.”

Jonathan Jones. “The Bizarre and Statistically Improbable Case of Eric Reid’s Random Drug Testing.” Sports Illustrated, Dec. 20, 2018

1.

What do you think of Reid’s claim? Do you believe that “more nefarious factors are afoot?” What information would be helpful to answer this question?

2.

An NFL team has around $71$ athletes on the roster if you count active players, reserve players, and practice squad players, so in any given week, there is about a $10 / 71$ chance that a player is selected randomly each week. Use your work from this unit to create an argument that supports or disputes Reid’s claim.

Part II

In a 2020 presidential poll conducted by the Monmouth University Polling Institute, they reported “If the presidential election were to happen today, Biden has the support of $48 %$ of registered voters and Trump has the support of $45 %$ .”

http://openup.org/qCsd7W

The poll also states, “The Monmouth University Poll was conducted by telephone from March 18 to 22, 2020 with $754$ registered voters in the United States and [has] a $\pm 3.6$ percentage point sampling margin of error. The poll was conducted by the Monmouth University Polling Institute in West Long Branch, NJ.”

3.

Explain the meaning of the $\pm 3.6$ percentage point margin of error in the context of the study.

4.

The article states “Joe Biden holds a negligible $3$ -point lead over Donald Trump in the race for president.” Explain why the article calls the lead negligible.

5.

Calculate the margin of error for this study and compare it to the one listed in the report.

6.

Compute the margin of error if the support for Biden was $48 %$ and Trump was $45 %$ and the sample was $2,000$ instead. If the results were based on a sample of $2,000$ instead of $754$ , would this change your response to problem 4? Explain.

Ready for More?

What are some of the first questions to ask when evaluating a claim in the media that is based on statistics?

Takeaways

Important ideas of statistics:

Lesson Summary

In this lesson, we evaluated statistical claims from media sources. We found that we need to pay attention to sample size and methods and compare the plausible intervals when drawing conclusions.

Retrieval

1.

Graph each complex number on the same complex plane. Let the point be the terminal point of a vector with the initial point being at the origin. Label each vector using vector notation.

$\overset{⇀}{p} = 4 + 6 i$
$\overset{⇀}{q} = - 10 + 4 i$
Graph $\overset{⇀}{p} + \overset{⇀}{q}$

2.

Coordinate Conversion:

The polar coordinates $(r, θ)$ are related to the rectangular coordinates $(x, y)$ as follows:

$r^{2} = x^{2} + y^{2} x = r \cos θ y = r \sin θ \tan θ = \frac{y}{x}$

a.

Convert point $W$ from polar to rectangular coordinates. $W = (5, \frac{7 π}{4})$

b.

Convert point $Z$ from rectangular to polar coordinates. $Z = (- 5, 12)$