2021 Live Review 7 | AP Statistics | Taming the Investigative Task on the AP Statistics Exam

In this session, Luke Wilcox, an AP Statistics teacher, welcomes students to the seventh live review of AP Statistics, focusing on the Investigative Task, a critical free-response question on the AP exam. He emphasizes the potential of this question to significantly boost students' AP scores and outlines five strategies to tackle it effectively. The session includes logistical information about accessing materials and gathering feedback, as well as addressing common questions from previous sessions, such as the difference between binomial and geometric random variables and conditions for statistical inference.

The paragraph delves into the specifics of the Investigative Task, its significance in the AP exam, and the general approach to tackle it. It discusses the importance of understanding the random condition in sampling and experiments, the 10% condition for sampling without replacement, and conditions for a normal sampling distribution. The summary also touches on the importance of checking these conditions in inference procedures like confidence intervals and significance tests, and it highlights the need for students to be familiar with these concepts to successfully complete the Investigative Task.

This section provides a detailed overview of the strategies to excel in the Investigative Task. It starts with a reminder to stay calm when encountering unfamiliar questions, as the task is designed to present new scenarios. The summary explains the importance of recognizing that the task will cover various units from the course and the necessity of securing points on the easier parts before tackling more complex sections. It also advises making educated guesses if stuck and the value of referencing previous answers in the final summary part of the task.

The speaker illustrates the application of the discussed strategies by analyzing an Investigative Task from the 2009 AP exam. The task involves assessing the average fuel efficiency of a car model, and the summary walks through defining the parameter of interest, stating null and alternative hypotheses, and identifying the type of inference procedure required. It also addresses common student errors in hypothesis formulation and emphasizes using the correct terminology when referring to population parameters.

This paragraph examines the process of hypothesis testing when faced with skewed distributions, using a scenario where the mean may be affected by outliers. It discusses the use of the sample mean to median ratio as an indicator of skewness and explains how a ratio greater than one suggests a right-skewed distribution. The summary also covers the concept of simulated sampling distributions to assess the plausibility of a normal population distribution, introducing the idea of estimating p-values from simulated data.

The speaker introduces a method to define a statistic for measuring skewness using the five-number summary from a data set. The summary explains how to create a box plot to visualize the distribution and suggests a statistic based on the ratio of the distances from the median to the maximum and minimum values. It emphasizes that a ratio greater than one indicates a right-skewed distribution and acknowledges that there are multiple correct ways to define such a statistic.

This section discusses Emma's investigation into the rental prices of one-bedroom apartments, focusing on the appropriate population for generalizing her sample results. The summary explains the concept of random sampling and its representativeness of the population, and it identifies the specific population that Emma's sample can be generalized to, which is one-bedroom apartments listed on a particular website by voluntary posters.

The speaker highlights the disadvantages of using the mean as an estimate of typical rental prices when the distribution is skewed to the right. The summary explains that the mean can be significantly larger than the median due to the influence of outliers, making the median a more accurate representation of typical prices. It emphasizes the importance of using the median to avoid overestimating typical rental prices.

This paragraph explores the process of developing a theoretical sampling distribution for the sample median, even without prior knowledge of bootstrapping. The summary explains the concept of obtaining every possible sample and calculating the median to build the sampling distribution. It also addresses the practical approach of using bootstrapping to approximate this distribution by taking random samples with replacement and calculating the median of each.

The speaker demonstrates how to calculate percentiles from a bootstrap distribution and use them to construct a confidence interval for the median rental price. The summary details the steps to find the fifth and ninety-fifth percentiles and the percentage of bootstrap medians between these values. It concludes with the interpretation of a 96% confidence interval for the median rental price, emphasizing the importance of context in the interpretation.

In the final paragraph, the speaker reflects on the session's objectives and the strategies discussed for tackling the Investigative Task. The summary reviews the importance of perseverance, understanding sampling distributions, and the significance of statistical inference in these tasks. It also highlights the value of the session in reducing anxiety around the Investigative Task and building confidence for the AP exam, inviting feedback for further improvement.