Question 3: Inference
How students get to school (chi-square test)
- Units 1 and 3
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A complete hypothesis test or confidence interval: you identify the variables, name the procedure, state hypotheses and parameters, check the conditions, do the calculations, and justify a conclusion in context. It uses the inference skills from Practices 2, 3 and 4. On the exam: Question 3 of 4 (official name: Inference (Hypothesis Test or Confidence Interval)). 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 D, and label any subparts (for example, i and ii).
The transportation survey
A school district has three high schools: Northside (1,400 students), Central (1,250 students) and Lakeview (1,520 students). A transportation planner selected independent random samples of 120 students from Northside, 110 students from Central and 120 students from Lakeview, and recorded each student's main way of getting to school. The results are in the table.
At the α = 0.05 significance level, complete the appropriate inference procedure to determine whether there is convincing statistical evidence that the distribution of main way of getting to school differs among the three high schools.
Source: Hypothetical scenario
Main way of getting to school
| School | Bus | Car | Walk or bike | Total |
|---|---|---|---|---|
| Northside | 46 | 38 | 36 | 120 |
| Central | 62 | 30 | 18 | 110 |
| Lakeview | 40 | 52 | 28 | 120 |
| Total | 148 | 120 | 82 | 350 |
Source: Hypothetical data
Suggested time: 22 minutes
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Part (A)
2 pointsIdentify and classify the variables in the study.
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Part (B)
1 pointIdentify the appropriate inference procedure.
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Part (C)
5 pointsComplete the inference procedure. Include the hypotheses, the populations, a check of the conditions, and the test statistic, degrees of freedom and p-value.
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Part (D)
2 pointsJustify a conclusion in context.
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