Question 2: Analyzing data and interpreting results

Main news source by age group

Units 1 and 2
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 news survey

A random sample of 500 adults in a town were asked their age and their main source of news. The table summarizes the responses. Each adult chose exactly one main source.

Source: Hypothetical scenario

Age group and main news source

Age group	Social media	Television	Print or news website	Total
18–29	78	22	30	130
30–49	64	58	68	190
50 and older	28	104	48	180
Total	170	184	146	500

Source: Hypothetical data

Suggested time: 22 minutes

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Part (A)

3 points

One adult from the sample is selected at random. (i) Calculate the probability that the adult's main news source is social media. (ii) Calculate the probability that the adult's main news source is social media, given that the adult is 18–29 years old. (iii) Calculate the probability that the adult is 18–29 years old or that the adult's main news source is social media.

Your answer to part (A)

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Part (B)

2 points

Determine whether the events "the adult is 18–29 years old" and "the adult's main news source is social media" are independent. Justify your answer.

Your answer to part (B)

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Part (C)

1 point

Two different adults are selected at random from the 500 adults in the sample, without replacement. Calculate the probability that both adults' main news source is print or a news website.

Your answer to part (C)

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Part (D)

2 points

(i) Describe a segmented bar chart that shows the distribution of main news source for each age group. Include what each bar represents and the values that determine the segments. (ii) Based on the chart, describe the association between age group and main news source.

Your answer to part (D)

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Part (E)

1 point

A reporter writes that the survey shows getting older causes people to switch from social media to television. Explain why this conclusion is not justified.

Your answer to part (E)

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Part (F)

1 point

One adult from the sample is selected at random. Calculate the probability that the adult's main news source is social media or television, and explain why the events "social media" and "television" can be handled as mutually exclusive.

Your answer to part (F)

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