Question 2: Analyzing data and interpreting results

Battery life of two phone models

Unit 1
10 points
About 22 minutes

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

A multi-part question built on a data set or summary statistics: you calculate things like outlier fences, compare distributions, pick the right measure of center or spread, and justify a claim in context. It focuses on Practices 3 and 4. On the exam: Question 2 of 4 (official name: Multi-Focus on Practices 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 F, and label any subparts (for example, i and ii).

The battery test

A consumer group randomly selected 40 new phones of Model X and 40 new phones of Model Y. Each phone was fully charged and then played the same streaming video until the battery ran out. The battery life, in hours, was recorded for each phone. The table shows summary statistics.

Source: Hypothetical scenario

Battery life (hours)

Model	n	Mean	SD	Min	Q1	Median	Q3	Max
X	40	11.6	2.9	4.1	10.2	12.0	13.4	16.0
Y	40	12.4	1.8	9.0	11.1	12.2	13.6	19.3

Source: Hypothetical data

Suggested time: 22 minutes

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Part (A)

2 points

Use the 1.5 × IQR rule to answer each part. Show your work. (i) Determine whether there are any outliers in the Model X data. (ii) Determine whether there are any outliers in the Model Y data.

Your answer to part (A)

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Part (B)

1 point

Use the summary statistics to describe the most likely shape of the distribution of battery life for Model X. Justify your answer.

Your answer to part (B)

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Part (C)

2 points

Compare the distributions of battery life for the two models. (i) Compare the centers. (ii) Compare the variabilities.

Your answer to part (C)

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Part (D)

1 point

A reviewer says the mean is the best measure of center for describing the battery life of Model X. Determine whether you agree with the reviewer. Justify your answer.

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Part (E)

2 points

(i) A Model Y phone in the sample lasted 15.0 hours. Use the 2-standard-deviation rule to determine whether this phone's battery life is an outlier for Model Y. (ii) A Model X phone in the sample also lasted 15.0 hours. Which phone's battery life is more unusually high relative to its own model? Justify your answer with calculations.

Your answer to part (E)

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Part (F)

2 points

The consumer group decides to report battery life in minutes instead of hours. (i) Calculate the mean and the IQR of Model X's battery life in minutes. (ii) Explain what happens to the z-score of the Model X phone that lasted 15.0 hours when the data are converted to minutes.

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