Question 3: Inference
Daily screen time (interval for a mean)
- 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 screen-time study
A counselor at a high school with 2,100 students selected a random sample of 45 students. Each student used their phone's screen-time report to record their average daily recreational screen time over the past week, in hours. The sample mean was 7.0 hours and the sample standard deviation was 2.6 hours. A dotplot of the 45 values is moderately skewed to the right with no outliers.
The principal claims that the mean daily recreational screen time for all students at the school is at least 8 hours. Construct and interpret a 95% confidence interval to evaluate the principal's claim.
Source: Hypothetical scenario
Suggested time: 22 minutes
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Part (A)
2 pointsIdentify and classify the variable 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 principal's claim is supported. Justify your answer.
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