• When introducing the lesson context, it’s helpful to emphasize how dramatically different the NBA Bubble atmosphere was from a typical stadium atmosphere. Playing regulation games on a closed court without 20,000 screaming fans was an unprecedented experience in the NBA. In addition, ordinarily, visiting teams must travel, stay in hotels, and adjust to a new stadium locker room and routine. In the bubble, everyone was already staying in hotels. No one traveled. And the routine was different for everyone. Emphasizing how unusual it was to no longer have a true “home” team will motivate why the assumption of “no home court advantage” is the null (presumed) hypothesis. Then, the fact that the “home” teams won more games will seem surprising. But how surprising was it? That’s what the results of the hypothesis test will reveal.
• This lesson builds directly on the earlier introduction to hypothesis testing in lesson 4.3 and formalizes the structure of a one-sample z-test for a population proportion. Drawing frequent connections back to the simulation-based results from the prior lesson will help students gain conceptual understanding of the mathematical results in this lesson.
• Similarly, frequently using “in a world where” phrasing can be helpful for building intuitive understanding. “In a world where there is no home court advantage, how surprising would it be for the home teams to win 56% or more of the games?” Every step of hypothesis testing can be framed as answering this type of “in a world where” question.

First, download this lesson's slide deck and handout key to see the prompt and sample responses for the Lesson Starter. Then, check out the additional background notes below.

Instructional routine: Ten-Minute Talk. The lesson provides space for students to jot down their thoughts on the prompt before discussing with a partner and engaging in whole group discussion. You can find more background on implementing a Ten-Minute talk here.

Purpose & Background: The card shark situation helps students explore the logic of hypothesis testing. If you assume the deck is fair (null hypothesis), you can judge how unusual the result (the observation) is. With 50% red cards in the deck and with the cards being replaced after each draw, P(all 5 draws are red) = (0.5)5= 3.1%. When a result is unusual enough (usually below the 5% significance level), we reject the null hypothesis. In this case, we reject the null hypothesis of a fair deck become convinced of the alternative: that the deck is unfair and may be stacked with only red cards. Students need not do precise calculations for the probability to recognize and justify their reasoning that this event is unlikely; however, doing so can provide a nice review of the multiplication rule and independent events from the prior unit (Unit 3: Probability).

Note: Instructors can consider doing a “live” version of this Lesson Starter. Come to class with a deck of only red cards. The instructor can play the role of the card shark and ask a student volunteer to play the game, with the rest of the class watching and evaluating the results.

First, download this lesson's Handout Key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• Generally, one-sided hypothesis tests are more common than two-sided hypothesis tests. This is because most researchers have a preconceived theory about the direction of an effect.
• Two-sided hypothesis tests tend to be used when …
• Stakeholders care about whether or not there is any significant difference from the null value, regardless of direction. For example, a computer chip manufacturing plant may need the conductivity of its chips to precisely match an ideal value. A two-sided hypothesis test could be performed with a random sample of chips to see if their conductivity is significantly lower or higher than the ideal value.
• Regulations may require two-sided tests. For example, if a new medical drug is highly experimental, regulators may require a two-sided test – to detect whether the drug improves outcomes or has unintended adverse effects.

• The lesson context naturally raises questions about what factors ordinarily contribute to home-court advantage. Crowd noise, travel fatigue, familiar routines, and stadium environment were all dramatically altered during the bubble season, creating a setting that is useful for statistical investigation.
• Even though the NBA did not intentionally design an experiment for statistical purposes, the league effectively created a natural experiment by randomly assigning “home” and “away” designations during the bubble season.

• The phrase “convincing statistical evidence” in a question stem is an important signal that a hypothesis test is appropriate. Contrasting this language with words such as “estimate” or “approximate,” which are more commonly associated with confidence intervals, can help students choose the appropriate inference procedures later in the course.
• For hypothesis tests involving proportions, the standard error calculation uses p0 (the proportion value from the null hypothesis) rather than p̂ (the proportion value from the sample data). This reflects the assumption that the null hypothesis is true when constructing the null distribution.
• The z-test statistic measures how many standard deviations the observed sample proportion is above or below the null value. Connecting the z-test statistic to earlier work with z-scores reinforces that hypothesis testing extends familiar standardization ideas into an inference setting.
• In order to ensure that the normal curve model behind a z-test is appropriate, students have to check a set of conditions. These conditions are covered in the next lesson and, for now, should be assumed to be true.