Question 4: Multi-focus question

Grip strength training

Units 1 and 4
10 points
About 22 minutes

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

A multi-part question that pulls together several units, such as probability from a table, a summary statistic and an inference procedure, and asks you to calculate, interpret and justify a claim. It uses Practices 2, 3 and 4. On the exam: Question 4 of 4 (official name: Multi-Focus on Practices 2, 3, and 4). 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 grip-strength program

A fitness center wants to know how much a new 6-week hand-strength program improves grip strength. It randomly selected 15 of the 900 members who had signed up for the program. Each selected member's grip strength, in kilograms (kg), was measured before the program and again after it. The results are in the table.

Source: Hypothetical scenario

Grip strength (kg)

Member	Before	After
1	31.2	36.0
2	28.4	33.1
3	35.0	38.9
4	26.8	33.5
5	40.1	44.0
6	33.5	40.2
7	29.9	33.0
8	37.2	43.6
9	24.6	30.1
10	32.8	36.9
11	30.5	37.2
12	36.4	39.8
13	27.7	34.6
14	34.1	38.5
15	38.0	44.3

Source: Hypothetical data

Suggested time: 22 minutes

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Part (A)

1 point

Explain why a paired procedure, rather than a two-sample procedure, is appropriate for these data.

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Part (B)

1 point

Calculate the mean and standard deviation of the differences (after − before).

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Part (C)

1 point

Explain whether the sample data condition for a t-interval is met. Use the differences in your answer.

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Part (D)

2 points

(i) Identify the appropriate inference procedure for estimating the mean improvement in grip strength. (ii) Construct a 90% confidence interval for the mean improvement. Assume the randomization and 10% conditions are met.

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Part (E)

2 points

Interpret the interval from part D in context.

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Part (F)

2 points

The fitness center's advertisement says the program increases members' grip strength by more than 5 kg, on average. (i) Determine whether the interval from part D supports this claim. (ii) Explain your reasoning.

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Part (G)

1 point

Explain why the fitness center cannot conclude from this study that the program caused the increase in grip strength.

Your answer to part (G)

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