• In framing the importance of reducing wait times for veteran mental health appointments, the beginning of the lesson mentions the issue of veteran suicides. Specifically, the lesson cites this statistic from a recent VA report: that the US averages 17 veteran suicides per day. Although awareness of this issue is incredibly important, when considering whether to mention this specific statistic in class, instructors should also take precautions to avoid resurfacing trauma. Specifically, we recommend giving students an anonymous survey (on paper or digitally) before this lesson, asking students whether discussion of data related to suicide (from a public health perspective) would resurface trauma. If any anonymous survey response says “yes,” we recommend not mentioning the data related to suicides. Ultimately, the lesson and its most leveraged data set – the data set of wait times for mental health appointments – does not require discussion of suicide statistics.
• This lesson revisits and builds on the VA wait times context from Lesson 2.B.5. However, this lesson also does not depend on students having prior experience with Lesson 2.B.5. So, instructors who have not used Lesson 2.B.5 can still successfully use this lesson. That said, instructors who have used Lesson 2.B.5 can potentially shorten some of the initial contextual information shared at the beginning of the lesson, as students will already be familiar with some of the contextual material from earlier in the school year.
• As students compare populations, samples, and sampling distributions in this lesson, it’s helpful to ask them: “Does this distribution show data values, or does it show means of data values?” This reinforcement will help students distinguish population and sample distributions (distributions of data values) from sampling distributions (distributions of means or other statistics).

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.

• Encourage students to explain the discussion question using both intuition and mathematics. The simulation helps build intuition that unusually high or unusually low observations have less influence when they occur in larger samples, while the formula explains the same phenomenon algebraically. Connecting these two perspectives strengthens students’ conceptual understanding.
• Highlight that the simulation and the formula describe the same statistical phenomenon from different perspectives. The simulation provides empirical evidence for how sample means behave, while the formula provides the theoretical model. Recognizing this connection helps bridge informal and formal statistical reasoning.

• For additional framing for the lesson context, consider sharing this video report about the original 2014-2015 VA wait time scandal. In addition to providing interviews and perspectives from veterans, the video includes a quote from the head of the VA claiming a 3-day average wait time for mental health appointments. The lesson centers around investigating this claim of a 3-day average wait time.
• The data for this lesson was gathered in 2022 by randomly sampling from the online VA Wait Time database, similarly to how students sampled from this database in Lesson 2.B.5. However, there is one difference. For Lesson 2.B.5, students randomly sampled geographic locations across the continental United States (via randomly chosen longitudes and latitudes). Then, they found the VA clinics located closest to their randomly sampled geographic locations. The sample obtained for this lesson was a simple random sample from a comprehensive list of all VA clinics that provide mental health care services. Ultimately, both sampling methods obtain similar results.

• The conditions for inference about means closely parallel those for proportions, helping reinforce that statistical inference follows a common structure across different settings. The primary difference is the Normal/Large Sample condition. Rather than checking the Large Counts condition used for proportions, students now rely on assuming that the population data is approximately normal or that the sample size is large enough for the Central Limit Theorem to take hold. Under these conditions, they can justify that the sampling distribution for x̄ is approximately normal.
• Sampling distributions provide the conceptual bridge between descriptive statistics and statistical inference. Rather than asking whether a single sample mean is “large” or “small,” students now evaluate whether a mean is “unusual” relative to a sampling distribution.
• Students can use the lesson applet to see the Central Limit Theorem in action by selecting different population shapes and sample sizes, then repeatedly clicking “add 100 samples” to build the distribution of sample means. As more samples are added, students can observe the sampling distribution becoming approximately normal. They can also see that larger sample sizes produce narrower sampling distributions, reinforcing the idea that larger samples lead to less variability.