Question 3: Inference
Text or email reminders (interval for two proportions)
- 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 reminder experiment
A public library wanted to know whether text-message reminders work better than email reminders at getting borrowed books returned on time. For 400 patrons with books due in the same week, the library randomly assigned 200 to receive a text reminder two days before the due date and the other 200 to receive an email reminder.
Of the 200 patrons who received a text, 172 returned their books on time. Of the 200 patrons who received an email, 151 returned their books on time.
The library director claims that, for patrons like those in the study, text reminders lead to a higher on-time return rate than email reminders. Construct and interpret a 95% confidence interval to evaluate the director's claim.
Source: Hypothetical scenario
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)
4 pointsComplete the inference procedure. Include a definition of the parameter, a check of the conditions, and the interval.
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Part (D)
3 points(i) Interpret the interval in context. (ii) Use the interval to determine whether the director's claim is supported. Justify your answer.
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