AP Statistics 7.10 Skills Focus: Selecting, Implementing, and Communicating Inference Procedures- MCQs - Exam Style Questions
▶️ Answer/Explanation
1. Analyze the Study Design:
The study measures the blood pressure of each of the 40 men twice: once before the treatment and once after. Because the two measurements are taken from the same subject, the data are not independent; they are paired.
2. Determine the Type of Data:
Blood pressure is a quantitative measurement, not a proportion or categorical count. The goal is to investigate the “change, on average,” which points to a test involving means.
3. Select the Correct Statistical Test:
– Tests for proportions (A, B) and categorical data (E) are incorrect.
– A two-sample t-test (C) is used for comparing the means of two independent groups. This is incorrect because our “before” and “after” groups are dependent.
– A matched-pairs t-test for a mean difference (D) is the appropriate procedure. This test analyzes the differences between the paired measurements for each subject (e.g., $BP_{after} – BP_{before}$) to determine if the average difference is statistically significant.
✅ Answer: (D)
▶️ Answer/Explanation
1. Margin of Error (ME) Formula:
\(ME = z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)
2. Analyze the Relationship:
Since \(z^*\) and \(\hat{p}\) are the same for both samples, the ME is proportional to \(\frac{1}{\sqrt{n}}\).
– \(ME_R \propto \frac{1}{\sqrt{1000}}\)
– \(ME_S \propto \frac{1}{\sqrt{4000}}\)
3. Compare the Margins of Error:
To find the relationship, take the ratio:
\(\frac{ME_R}{ME_S} = \frac{1/\sqrt{1000}}{1/\sqrt{4000}} = \frac{\sqrt{4000}}{\sqrt{1000}} = \sqrt{\frac{4000}{1000}} = \sqrt{4} = 2\)
Therefore, \(ME_R = 2 \times ME_S\).
✅ Answer: (E)