• 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 3.A.6 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 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. For example, if biostatisticians are researching whether a drug lowers blood pressure, they will set up a one-sided test in which the alternative is that blood pressure is lower than normal. There is little reason to also test whether the drug increased blood pressure.
• Two-sided hypothesis tests are generally only 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 used on a random sample of chips to see if their conductivity is significantly lower or higher than the ideal value.
• Regulations require two-sided tests. For example, if the blood pressure drug mentioned above is highly experimental, regulators may require a two-sided test — to detect if the drug may have an unforeseen adverse effect and actually raise blood pressure.

• 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. For this reason, as with all experiments, we don’t need to check the 10% condition during the inference procedure. When treatments are randomly assigned, independence is satisfied.

• The phrase “convincing statistical evidence” 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 select appropriate inference procedures later in the course.
• For hypothesis tests involving proportions, the standard error calculation uses p₀, the value from the null hypothesis, rather than p̂ 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 can help reinforce that hypothesis testing extends familiar standardization ideas into an inference setting.
• The conditions for inference are used to justify modeling the sampling distribution with a normal curve. Framing conditions as supporting the validity of the model, rather than as a checklist to memorize, can help students better understand their purpose.