AP Statistics: Worth the Weight? (Part 2)
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 1 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 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 In an earlier lesson, we met the Kiddle team that was trying to establish the mean weight of all books that kids aged 8-12 years read. Here is a quick recap of what we did: We reviewed the data obtained by the Kiddle team regarding the weights of 10 randomly selected books from their nearby public library. We identified that the mean weight of their random sample of books was 284.6 g, while the assumed mean is considered to be 260 g. We modified the weights of the books in their sample, to obtain the ‘modified weight’ of books, which share the same variability as the original sample but has a mean equal to the assumed mean. We resampled from the original sample with replacement (keeping sample size the same, ie, 10) and generated a distribution of sample means. We will now see what we can learn from this. First, let’s resample again.
Topics and standards: Math, Statistics & AP Statistics, Tools Lab, Assessment, Inference on Quantitative Data, AP Statistics