Subjects statistics

Confidence Interval Width 42F15E

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1. **State the problem:** We are given a 90% confidence interval for a population proportion with a sample proportion of 18% and a margin of error of 4%. We need to find the width of the confidence interval. 2. **Recall the formula for a confidence interval for a population proportion:** $$\text{Confidence Interval} = \hat{p} \pm \text{Margin of Error}$$ where $\hat{p}$ is the sample proportion. 3. **Important rule:** The width of the confidence interval is twice the margin of error because the interval extends equally above and below the sample proportion. 4. **Calculate the width:** $$\text{Width} = 2 \times \text{Margin of Error} = 2 \times 4\% = 8\%$$ 5. **Interpretation:** The confidence interval spans 8 percentage points in total. **Final answer:** The width of the confidence interval is 8 percent.