Aim for FiveStatistics

Question 1: Formulating questions and collecting data

Reaction time with each hand

  • Units 1, 3 and 4
  • 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 reaction-time study

A physical education teacher wonders whether students react faster with their dominant hand than with their nondominant hand. She randomly selects 30 of the 1,100 students at her school.

Each selected student does a ruler-drop test with each hand. A partner holds a ruler and lets go without warning, and the student catches it between thumb and finger. The distance the ruler falls before it is caught is recorded in centimeters (cm); a shorter distance means a faster reaction. For each student, a coin flip decides which hand is tested first.

For each student, d = (distance with the dominant hand) − (distance with the nondominant hand).

Source: Hypothetical scenario

Suggested time: 22 minutes

Your answers are saved in this browser as you type.

Something wrong with this question?

What's wrong?

Please don't include personal details.

Part (A)

1 point

Identify the explanatory variable and the response variable in this study.

0 / 2,500 characters

Part (B)

2 points

(i) Identify the type of design used in this study. (ii) Explain why this design is better for answering the teacher's question than randomly dividing the 30 students into two groups of 15 and testing one group with dominant hands and the other with nondominant hands.

0 / 2,500 characters

Part (C)

1 point

Explain the purpose of using a coin flip to decide which hand each student uses first.

0 / 2,500 characters

Part (D)

1 point

Identify the appropriate inference procedure for testing whether the mean catch distance is shorter for the dominant hand than for the nondominant hand.

0 / 2,500 characters

Part (E)

2 points

(i) Define the parameter of interest in context. (ii) State the null and alternative hypotheses for the test.

0 / 2,500 characters

Part (F)

2 points

(i) Describe a Type I error in the context of this test. (ii) Describe a Type II error in the context of this test.

0 / 2,500 characters

Part (G)

1 point

Explain why the teacher can generalize the results of this study to all students at her school.

0 / 2,500 characters

Checking scoring…

Scoring it yourself shows you the rubric, examples and a model answer. Try writing your answer first.