AP Statistics: Worth the Weight? (Part 1)
Task
Lesson Purpose This lesson introduces the concepts of bootstrapping and hypothesis testing to students in a scaffolded manner, helping them look under the hood of some fairly opaque but extremely powerful statistical methods. It also lays bare the assumptions that are made along the way, helping students understand when these statistical processes can or cannot be used. This lesson works best when paired with part 2 of the same title. Narrative In this lesson, students will: Shift a random sample’s data points to an assumed mean while maintaining its variability. Resample from a given sample with replacement to generate a distribution of sample means. Raise questions regarding the nature of the distribution of sample means. Standards This lesson (and the next) addresses the following AP Statistics course standards: UNC-3.H: Estimate sampling distributions using simulation. UNC-3.S: Interpret probabilities and parameters for a sampling distribution for a sample mean. VAR-7.C: Identify the null and alternative hypotheses for a population mean. DAT-3.E: Interpret the p-value of a significance test for a population mean. DAT-3.F: Justify a claim about the population based on the results of a significance test for a population mean. How Tuva Enhances This Activity Bootstrapping (vs t-statistic): Unlike most hypothesis testing lessons that start with t-statistic, this one starts with bootstrapping, making the rationale of hypothesis testing much clearer to students. Visualizing Probabilities: Students visualize how sample means stacked up, and how likely a specific value of the sample mean is.
Introduction An electronics company wishes to design a Kindle-like device specifically for young readers aged 8-12. years. They haven’t decided on a name for the device yet, but internally they are calling it Kiddle. They want their device to be significantly lighter than the average weight of a physical book. Therefore, the team designing Kiddle has a pertinent question to answer: “What is the weight of an average book that an 8-12-year-old reads?” Let’s see how they can arrive at a fair number.
Topics and standards: Math, Statistics & AP Statistics, Assessment, Inference on Quantitative Data, AP Statistics