Aim for FiveStatistics

Question 1: Formulating questions and collecting data

Tree cover and park temperatures

  • Units 1 and 5
  • 10 points
  • About 22 minutes

You can use a calculator on this question, just like on exam day.

A multi-part question about a study's design: you identify sampling methods or study types, explain whether results can be generalized or show cause and effect, describe or choose a display, and write a valid investigative question. It focuses on Practices 1 and 2. On the exam: Question 1 of 4 (official name: Multi-Focus on Practices 1 and 2). Section II has 4 free-response questions in 90 minutes (50% of the score); each question is worth 10 points and 12.5% of the score. The exam is fully digital in Bluebook, a graphing calculator with statistical capabilities is expected, and the formula sheet and tables are provided.

The question and its sources

Show the work that leads to each answer, and explain your reasoning in the context of the situation. A graphing calculator with statistical capabilities, the formula sheet and the statistical tables are available. Use the information given to answer parts A through G, and label any subparts (for example, i and ii).

The park study

A city has 84 public parks. The parks department classifies each park by size: 40 are small, 28 are medium and 16 are large.

An urban planner wants to study the relationship between the percent of a park's area covered by tree canopy and the park's average ground-surface temperature, in degrees Celsius (°C), on summer afternoons. She plans to select 21 of the parks and measure both variables at each one.

Source: Hypothetical scenario

Suggested time: 22 minutes

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Part (A)

2 points

(i) Identify the explanatory variable and the response variable. (ii) Classify each variable as categorical or quantitative. If it is quantitative, also classify it as discrete or continuous.

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Part (B)

2 points

(i) Identify a graphical representation appropriate for displaying the relationship between the two variables. (ii) Explain why the representation you identified in part B (i) is appropriate.

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Part (C)

1 point

Describe how the planner could select a stratified random sample of 21 parks, using park size as the strata, so that each size group is represented in proportion to the number of parks of that size.

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Part (D)

1 point

Explain one reason that stratifying by park size could be beneficial in this study.

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Part (E)

2 points

(i) Identify the type of study the planner is conducting. (ii) The planner finds a strong negative correlation, r = −0.78, between tree canopy and temperature. Explain why she cannot conclude that more tree canopy causes lower park temperatures. Include a possible confounding variable in your explanation.

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Part (F)

1 point

The planner's assistant measured the temperature at some parks at 1:00 p.m. and at other parks at 5:00 p.m. Explain why this could be a problem, and describe how to fix it.

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Part (G)

1 point

Suppose the planner selects the stratified random sample described in part C. Explain to which parks the results of this study can be generalized.

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