Question 4: Multi-focus question
Strep tests at a school clinic
- Units 2 and 3
- 10 points
- About 22 minutes
You can use a calculator on this question, just like on exam day.
A multi-part question that pulls together several units, such as probability from a table, a summary statistic and an inference procedure, and asks you to calculate, interpret and justify a claim. It uses Practices 2, 3 and 4. On the exam: Question 4 of 4 (official name: Multi-Focus on Practices 2, 3, and 4). 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 strep test
At a school health clinic, 15% of students who come in with a sore throat have strep throat. A rapid strep test gives a positive result for 90% of students who have strep throat and for 5% of students who do not have strep throat.
Source: Hypothetical scenario
Suggested time: 22 minutes
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Part (A)
2 pointsA student with a sore throat is tested. (i) Calculate the probability that the test result is positive. (ii) Calculate the probability that the student has strep throat, given that the test result is positive. Show your work.
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Part (B)
1 pointDetermine whether the events "the student has strep throat" and "the test result is positive" are independent. Justify your answer.
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Part (C)
6 pointsThe clinic serves two high schools. A nurse selected a random sample of 220 sore-throat visits from School A's clinic records over the past five years and an independent random sample of 210 sore-throat visits from School B's records. Each school had more than 3,000 sore-throat visits in that time. In the samples, 48 of School A's visits and 30 of School B's visits had a positive strep test. At the α = 0.05 significance level, the nurse wants to determine whether there is convincing statistical evidence that the proportion of sore-throat visits with a positive strep test differs between the two schools. (i) Identify the appropriate inference procedure. (ii) State the hypotheses, and define the parameters. (iii) Check the normality condition. (iv) Calculate the test statistic and p-value. (v) Compare the p-value with α, and make a decision about the null hypothesis. (vi) State your conclusion in context.
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Part (D)
1 pointBased on your decision in part C, identify the type of error that could have been made, and describe it in context.
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