• For daily class schedules (45-min class periods), this lesson can be completed in three days:
• Day 1: Activity from Part A (Detecting Parkinson’s with Scent)
• Day 2: Activity & Discussion from Part B (The “E-Nose”)
• Day 3: Practice, Mastery Check from Part B (The “E-Nose”)
• For block periods (90-minute class periods), the entire lesson can be completed in 1.5 class days.
• If using the optional Lesson 3.A.0, these activities can flow together as 4 days for daily class schedules of 2 full class days for block schedules.

• For Part A of the lesson, instructors can download the materials and view the full activity guidance at this page (from our friends at Math Medic). Note that instructors have to make a Math Medic account to download the materials. Much like Skew The Script, accounts with Math Medic are free.
• For Part B of the lesson, students complete the Amplify activity (with the instructor facilitating), as they record notes in their handout along the way. To facilitate an Amplify activity, instructors can create an Amplify account (also free) and share a single session code with their students (who can join without accounts).
• For facilitating the Amplify activity, we recommend using the “Sync to Me” pacing option. For more Amplify activity facilitation tips, check out our Amplify/Desmos session with expert Kevin McSorley.
• After the notes, students discuss the Discussion Question in small groups. Then, students discuss in full-group, with the instructor facilitating. Finally, students proceed to the Practice problems and, eventually, the lesson Mastery Check.

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.

• Emphasize that the goal of the discussion question is not to decide whether the “E-nose” did well, but to determine whether the results would be expected under random guessing. This shift from evaluating performance to evaluating probability is central to statistical reasoning.
• A key idea that arises in the Discussion Question is the impact of sample size on the spread of a sampling distribution. The connection between sample size and spread can be illustrated two ways:
• With the sampling distribution formula: In the formula for the standard deviation of the sampling distribution, the sample size is in the denominator. So, as n increases, we divide by a larger number, thereby shrinking the standard deviation value.
• With the law of large numbers and intuition: If we flip a fair coin only twice, there’s a sizable chance that 100% of those flips will be Heads. If we flip the coin 1,000 times, getting 100% Heads is almost impossible. Instead, the proportion of flips that come up Heads will likely be very close to the true probability: 50%. This is the law of large numbers (from our earlier probability unit) at work, and it also applies to sampling. With a very high sample size, our estimates will be tightly clustered around the true probability or proportion value. With a lower sample size, there’s more variation. This is why higher sample sizes produce more precise sampling distributions.

• The Zhejiang University study suggests that Parkinson’s disease is associated with a distinct chemical “fingerprint” in skin oils, likely tied to metabolic and microbiome changes – and that this signal may be detectable before clear motor symptoms appear.
• In preliminary studies, the model was able to reliably distinguish Parkinson’s patients from healthy controls. While this points to strong potential for early-stage, scalable screening, the approach remains in the research and validation phase, with no approved clinical devices yet. Ongoing studies are focused on confirming whether these findings hold across larger, more diverse populations before moving toward real-world use.

• This lesson continues to use simulation, but it also introduces formulas and calculations that will form the basis of hypothesis testing and confidence intervals in upcoming lessons. Because of the higher degree of abstraction introduced in this lesson, students may start to lose their bearings. If this occurs, continue returning to the logical foundations of sampling variation and extreme results that have been established in the last few lessons, using the results of simulations as concrete examples.
• To support students as they begin working with calculations for the sampling distribution of a proportion, reinforce that sampling distributions are composed of many statistics, rather than many data values. This is illustrated by the graphic included in the handout showing many p̂ values under the normal curve.
• For AP Statistics, students are not expected to be able to derive the standard deviation formula for the sampling distribution of a proportion. Focus on interpretation and application rather than derivation. However, for students who are curious, consider sharing this supplemental video, which shows how the formula \( \sqrt{\frac{p(1-p)}{n}} \) comes from the standard deviation of the binomial distribution. The video is tied to the next lesson but can be shared alongside this lesson for especially curious students.
• Point out that the formulas for the mean and standard deviation of a sampling distribution of a proportion are provided in the AP Statistics formula booklet. This means that students should focus on understanding the concepts and applications of these formulas rather than memorizing them.