Aim for FiveStatistics

Question 1: Formulating questions and collecting data

Three plans for a library survey

  • Unit 1
  • 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 E, and label any subparts (for example, i and ii).

The library survey

A city's library system serves about 48,000 households, which are spread across 6 districts. The library board wants to learn how households use the libraries. The survey will ask how many times members of the household visited any city library in the past month and whether anyone in the household has a library card.

Three plans for choosing households have been proposed.

Plan 1: A link to an online survey is posted on the library system's home page for two weeks. Anyone who visits the home page can fill it out.

Plan 2: Using the city's list of all household addresses, sorted by district, the board selects a simple random sample of 150 households from each of the 6 districts.

Plan 3: The city has 240 residential blocks. The board numbers the blocks from 1 to 240, uses a random number generator to select 12 different blocks, and surveys every household on those 12 blocks.

Source: Hypothetical scenario

Suggested time: 22 minutes

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Part (A)

2 points

(i) Identify the sampling method used in Plan 2. (ii) Identify the sampling method used in Plan 3.

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Part (B)

2 points

(i) Explain why the results of Plan 1 should not be generalized to all households in the city. (ii) A board member says that, if library use differs a lot from district to district, Plan 2 will tend to give a more precise estimate of the mean number of visits than a simple random sample of 900 households from the whole city. Explain why the board member is correct.

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Part (C)

2 points

The board wants to display the distribution of the number of library visits in the past month for the sampled households. (i) Identify a graphical representation that is appropriate for displaying this distribution. (ii) Explain why the graphical representation you identified in part C (i) is appropriate.

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Part (D)

1 point

A draft of the survey includes this question: "Given everything the library does for our community, don't you agree it deserves more funding?" Identify the type of bias this question could cause, and explain how it would likely affect the estimated proportion of households that support more library funding.

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Part (E)

3 points

A board member believes that the proportion of households with a library card is greater in District 1 than in District 4. Determine a valid investigative question for a study of this belief. Make sure your question includes all three components of a valid investigative question.

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