Question 3: Inference
Ride-share wait times (two-sample t-test)
- Units 1 and 4
- 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 wait-time study
A ride-share company wants to know whether the average wait time for a ride differs between two parts of a city, the Harbor district and the Hills district. From last month's records, it selected a random sample of 40 ride requests from the Harbor district and an independent random sample of 35 ride requests from the Hills district. Each district had more than 5,000 ride requests last month. The time from request to pickup, in minutes, was recorded for each sampled request.
At the α = 0.05 significance level, complete the appropriate inference procedure to determine whether there is convincing statistical evidence of a difference in the mean wait time for all of last month's ride requests in the two districts.
Source: Hypothetical scenario
Wait time (minutes)
| District | n | Mean | SD |
|---|---|---|---|
| Harbor | 40 | 7.8 | 3.1 |
| Hills | 35 | 9.6 | 4.2 |
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, a definition of the parameters, a check of the conditions, and the test statistic and p-value.
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Part (D)
2 pointsJustify a conclusion in context.
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