 Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line.

(Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest four decimal places).

95% confidence interval =

To compute the 95% confidence interval for the true proportion of Gastown residents living below the poverty line, we will use the formula for a confidence interval for a proportion. The formula is:

\[
\text{CI} = \hat{p} \pm Z_{\alpha/2} \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
\]

Where:
- \(\hat{p}\) is the sample proportion (the proportion of residents living below the poverty line in the sample),
- \(Z_{\alpha/2}\) is the Z-score corresponding to the confidence level (for 95%, \(Z_{\alpha/2} = 1.96\)),
- \(n\) is the sample size.

### Step-by-step procedure:

1. **Determine the sample proportion** (\(\hat{p}\)):
   \[
   \hat{p} = \frac{x}{n}
   \]
   where \(x\) is the number of residents living below the poverty line in the sample and \(n\) is the total sample size.

2. **Calculate the margin of error** (ME):
   \[
   \text{ME} = Z_{\alpha/2} \cdot \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}
   \]

3. **Construct the confidence interval**:
   \[
   \text{CI} = \left( \hat{p} - \text{ME}, \hat{p} + \text{ME} \right)
   \]

Once you provide the sample data (values for \(x\) and \(n\)), we can plug those into the formula to get the final 95% confidence interval.

Let me know if you have that data or need any clarifications!

Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest four decimal places).

Learn how to compute the 95% confidence interval for the true proportion of Gastown residents living below the poverty line using sample data. This problem involves statistical concepts like proportions, confidence intervals, and margin of error. Step-by-step solution provided with detailed intermediate steps.

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