AP Statistics 8.2 Setting Up a Chi-Square Goodness of Fit Test - MCQs - Exam Style Questions

1. Find the Sample Proportion ($\hat{p}$):
We are interested in residents who are “very supportive” or “somewhat supportive.”
Number of supportive residents ($x$) = $336 + 387 = 723$.
Total sample size ($n$) = $1,018$.
$\hat{p} = \frac{x}{n} = \frac{723}{1018} \approx 0.7102$

2. Determine the Formula and Critical Value ($z^*$):
The formula for a one-proportion confidence interval is: $\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$
For a 95% confidence level, the critical value $z^*$ is 1.96.

3. Calculate the Margin of Error (ME):
$ME = 1.96 \times \sqrt{\frac{0.7102(1-0.7102)}{1018}}$
$ME = 1.96 \times \sqrt{\frac{0.7102(0.2898)}{1018}}$
$ME = 1.96 \times \sqrt{0.000202} \approx 1.96 \times 0.0142 \approx 0.0279$

4. Construct the Interval:
The interval is approximately $0.71 \pm 0.028$.
✅ Answer: (E)