7 | FRQ (Part B, Question 6: Investigative Task) | Practice Sessions | AP Statistics

Summary

In this AP Stats Daily Practice Session, Mr. Starnes explores the investigative task, focusing on analyzing scatterplots and constructing graphical displays from two-way tables. He guides students through describing associations, calculating the chi-square statistic, and understanding the effects of data changes on correlation and chi-square values. By comparing the strengths and weaknesses of these statistical measures, he emphasizes the importance of context and careful analysis in drawing conclusions from data. This session equips students with essential skills for tackling complex statistical questions on the AP exam.

Takeaways

• 😀 The session focuses on the investigative task, the final question in the AP Statistics free response section.
• 📊 Students should review the associated scatterplot displaying house sizes and selling prices before watching the solution.
• 🔍 Part A emphasizes describing the association in a scatterplot, covering direction, form, strength, unusual features, and context.
• 🏠 A model response for describing the association includes identifying a strong positive linear relationship and mentioning an unusual point.
• 📈 In Part B, students are tasked with constructing a graphical display using a two-way table summarizing house classifications.
• ✏️ It's essential to label and scale axes correctly when creating graphs, indicating relative frequency and house size categories.
• 🧮 Part B also includes calculating expected values under the assumption of no association between size and price using totals from the table.
• 📉 Part C explores the effect of changing the selling price of a house on the correlation coefficient, noting that it weakens the linear relationship.
• 🔗 In Part C(ii), it is noted that the decrease in price does not change the house's classification in the two-way table, affecting the chi-square statistic.
• 💡 Part D encourages broader thinking about statistical concepts, contrasting the strengths and weaknesses of using chi-square versus correlation to measure association.

Q & A

What is the main focus of the practice session led by Mr. Starnes?

The main focus is on the investigative task, which is the final question in the free response section of the AP Statistics exam.

What does part a of the question ask students to describe?

Part a asks students to describe the association shown in a scatterplot that represents the size and selling price of houses.

What key elements should be included when describing the association in a scatterplot?

The key elements include the direction of the relationship, the form (linear or non-linear), the strength (strong, moderate, weak), any unusual features, and the context (names of the variables).

How many houses are considered large and expensive according to the two-way table?

According to the two-way table, 8 out of 12 large houses are considered expensive.

What type of graphical display should be constructed based on the two-way table?

A segmented bar graph should be constructed to represent the relative frequencies of expensive and not expensive houses for both large and not-large categories.

What does part b(ii) ask students to do regarding the expected number of houses?

Part b(ii) asks students to complete a table with the expected number of houses in each classification assuming no association between size and price.

What does the correlation coefficient (r) measure in the context of the scatterplot?

The correlation coefficient (r) measures the strength and direction of the linear association between size and selling price of the houses.

What effect does decreasing the price of the most expensive house have on the correlation coefficient?

Decreasing the price weakens the strength of the linear relationship, causing the correlation coefficient (r) to decrease and move closer to zero.

How does the decrease in price affect the chi-square statistic?

The decrease in price does not affect the chi-square statistic because the house remains categorized as large and expensive; therefore, its location in the two-way table does not change.

What are one benefit and one drawback of using chi-square instead of the correlation coefficient?

A benefit of using chi-square is that it is resistant to unusual values, meaning one outlier won't significantly impact the statistic. A drawback is that it treats all large or expensive houses the same, potentially losing some nuanced information about individual houses.