Free response · Unit 2 Beta

Transit use by home location: a two-way table

Q2: Analyze and interpret data · calculator allowed · 10 points

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The question

Name: ______________________   Date: ____________   Transit use by home location: a two-way table (10 points)

Table

Home location and weekly transit use

A regional transit agency surveyed a random sample of 500 adults in a metro area. Each adult reported where they live and whether they use public transit at least once a week. The results are in the table (invented data).
Home location and weekly transit use for 500 adults
Home locationUses transit weeklyDoes notTotal
Downtown9664160
Inner suburbs84116200
Outer suburbs28112140
Total208292500

  1. (a) An adult is selected at random from the 500 in the sample. (i) Calculate the probability that the adult uses transit weekly, given that the adult lives downtown. (ii) Calculate the probability that the adult lives downtown, given that the adult uses transit weekly. (iii) Explain why the two probabilities are different. [3 points]

  2. (b) Describe the association between home location and weekly transit use for the adults in the sample. Support your answer with appropriate calculations. [2 points]

  3. (c) For an adult selected at random from the sample, are the events "lives downtown" and "uses transit weekly" independent? Justify your answer. [2 points]

  4. (d) Calculate the probability that a randomly selected adult from the sample lives downtown or uses transit weekly. [1 point]

  5. (e) A city council member claims that adults who live downtown are more than twice as likely to use transit weekly as adults who live in the outer suburbs. Do the data support the claim? Justify your answer. [2 points]