Question 3: Inference
Free breakfast program (test for a proportion)
- 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 breakfast program
Last school year, 35% of the students at Ridgeview High School ate breakfast on most school mornings. This year the school, which has 2,150 students, began serving free breakfast in the cafeteria before first period.
To see whether the program is working, the principal selected a random sample of 160 students and asked each one whether they eat breakfast on most school mornings. Of the 160 students, 70 said yes.
At the α = 0.05 significance level, complete the appropriate inference procedure to determine whether there is convincing statistical evidence that the proportion of all students at the school who now eat breakfast on most school mornings is greater than 0.35.
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)
5 pointsComplete the inference procedure. Include the hypotheses, a definition of the parameter, 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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