Aim for FiveStatistics

Question 1: Formulating questions and collecting data

Music and typing speed experiment

  • 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 F, and label any subparts (for example, i and ii).

The typing experiment

A teacher wants to know whether listening to music affects how fast students type. Sixty students at her school volunteer. Each will take the same 5-minute typing test, which is scored in correctly typed words per minute (wpm).

Each volunteer will be assigned to one of three conditions: music with lyrics played through headphones, instrumental music played through headphones, or silence while wearing the same headphones. Twenty volunteers will be assigned to each condition.

Of the 60 volunteers, 24 have completed the school's keyboarding course and 36 have not.

Source: Hypothetical scenario

Suggested time: 22 minutes

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Part (A)

2 points

(i) Identify the experimental units in this study. (ii) Identify the treatments in this study.

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Part (B)

1 point

Describe how the teacher could randomly assign the 60 volunteers to the three conditions so that 20 volunteers are assigned to each condition.

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Part (C)

2 points

(i) Describe how the teacher could use a randomized block design based on whether volunteers have completed the keyboarding course. (ii) Explain why blocking on whether volunteers have completed the keyboarding course would be beneficial in this study.

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Part (D)

1 point

In the silence condition, volunteers still wear the same headphones, with nothing playing. Explain why this is a good feature of the design.

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Part (E)

2 points

(i) Explain whether the results of this experiment can be generalized to all students at the school. (ii) Suppose the mean typing speed for the lyrics group is much lower than for the silence group, and the difference is statistically significant. Explain whether the teacher can conclude that listening to music with lyrics causes students to type more slowly.

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Part (F)

2 points

The teacher believes that, on average, students type more slowly while listening to music with lyrics than while in silence. She wants to write a valid investigative question for this comparison. (i) Determine the second component of a valid investigative question for this comparison. (ii) Determine the third component of a valid investigative question for this comparison.

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