2022 Live Review 7 | AP Statistics | Tackling the AP Statistics Investigative Task

The session begins with an introduction by the instructor, Darren Starns, who welcomes AP Statistics students to the seventh live review session. He is located in Hilton Head, South Carolina, and has extensive experience as a teacher and exam reader for AP Statistics. The focus of this session is to address the AP Statistics investigative task. Students are advised to have specific materials ready, including a handout, formula sheet, and inference flowchart, all accessible through a provided URL. The handout is detailed, with hyperlinks to essential resources and questions that will be discussed during the session. The instructor emphasizes the importance of these materials and suggests that students download them if they haven't already. The session's goals are outlined: to review essential content and skills, share strategies for tackling the investigative task, and build students' confidence to maximize their exam scores.

The instructor discusses strategies for approaching the AP Statistics investigative task, which is known for its complexity and the requirement to apply skills in new contexts. The strategies include starting with familiar concepts, being prepared for unexpected twists, making up answers if stuck, summarizing understanding at various points, and managing time wisely. The session will involve working through two investigative tasks from past exams to illustrate these strategies. The tasks are designed to assess multiple skill categories and content areas, emphasizing application in non-routine ways. The instructor highlights the importance of not scoring zero on this task due to time management or lack of progress.

The first investigative task involves analyzing box plots and scatter plots of baseball game attendance data, comparing distributions and trends between an old and a new stadium. The task requires students to describe the shape, center, variability, and any unusual features of the distributions, as well as to compare trends over time. The instructor demonstrates how to apply the strategies discussed earlier, emphasizing the importance of starting with what is known and being prepared for the unexpected. The analysis includes interpreting box plots for distribution characteristics and scatter plots for trends, with a focus on the application of statistical concepts to real-world data.

The session continues with a deeper analysis of the baseball attendance data, focusing on the relationship between average attendance and the number of games won. The instructor guides students through describing the relationship using scatter plots and then introduces the concept of confounding variables. A confounding variable could be a third variable that affects the relationship between the two variables of interest. The task requires students to explain how one of the variables—number of games won—could be a confounding variable in the relationship between average attendance and other variables, such as the year or stadium. The instructor provides a detailed explanation and demonstrates how to connect graphical evidence to the concept of confounding.

The second investigative task shifts to a different context, examining the effectiveness of a new pain reliever formulation in reducing stomach irritation. The task involves a preliminary study with a randomized experiment and a significance test for comparing two proportions. The instructor outlines the steps for conducting the test, including stating hypotheses, identifying the procedure, performing calculations, and making a conclusion in context. The focus is on the correct application of inferential statistics to determine if there is evidence that the new formulation reduces stomach irritation at a 10% significance level.

The instructor provides a detailed walkthrough of performing the two-sample z-test for the pain reliever study, including the calculation of the test statistic and p-value. Two methods are demonstrated: using the formula sheet and using a graphing calculator. The results indicate whether there is sufficient evidence to support the claim that the new formulation reduces stomach irritation. The session emphasizes the importance of correctly interpreting the p-value in the context of the study and making an informed conclusion based on the data.

Following the significance test, the session explores the potential for Type I and Type II errors in the context of the study. The instructor explains the consequences of each error type and their implications for the drug company. Additionally, a simulation study is introduced to estimate the power of the test with an increased sample size. The histogram of p-values from the simulation is used to estimate the test's power, providing insight into the likelihood of correctly rejecting the null hypothesis under the assumed conditions.

The session concludes with an interpretation of the estimated test power obtained from the simulation study. The value represents the probability of correctly rejecting the null hypothesis when the alternative is true, given the assumptions about the true proportions of stomach irritation for the two medications. The instructor emphasizes the importance of understanding what the power estimate signifies in the context of the study and how it relates to the research question and the potential impact on the drug's marketing and patient treatment.

In the final part of the session, the instructor recaps the key content and skills addressed, including comparing distributions, describing relationships, identifying confounding variables, performing significance tests, and estimating test power. The strategies discussed earlier in the session are reiterated, with an emphasis on starting with known concepts, preparing for unexpected twists, making up answers if necessary, summarizing, and managing time effectively. The instructor thanks the students for their participation and encourages them to attend the final session for additional strategies and tips. The session aims to build students' confidence and equip them with the skills to tackle investigative tasks effectively on the AP exam.