Questions: The figure to the right shows the results of a survey in which 996 adults from Country A, 1008 adults from Country B, 999 adults from Country C, 1005 adults from Country D, and 1006 adults from Country E were asked whether national identity is strongly tied to birthplace. National Identity and Birthplace People from different countries who believe national identity is strongly tied to birthplace Country A 36 % Country B 22 % Country C 27 % Country D 51 % Country E 14 % Construct a 95% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. The 95% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is . 1 ). (Round to three decimal places as needed.)

Solution Steps

To calculate the 95% confidence interval for the proportion of adults from Country A who believe national identity is strongly tied to birthplace, we use the sample proportion \(\hat{p} = 0.36\) and the sample size \(n = 996\).

The formula for the confidence interval is given by:

\[ \hat{p} \pm z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]

Where \(z\) is the z-score corresponding to the 95% confidence level, which is approximately \(1.96\).

Calculating the margin of error:

\[ \text{Margin of Error} = 1.96 \cdot \sqrt{\frac{0.36(1 - 0.36)}{996}} \approx 0.03 \]

Thus, the confidence interval is:

\[ 0.36 \pm 0.03 = (0.33, 0.39) \]

For Country B, the sample proportion is \(\hat{p} = 0.22\) and the sample size is \(n = 1008\).

Using the same formula for the confidence interval:

\[ \hat{p} \pm z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]

Calculating the margin of error:

\[ \text{Margin of Error} = 1.96 \cdot \sqrt{\frac{0.22(1 - 0.22)}{1008}} \approx 0.013 \]

Thus, the confidence interval is:

\[ 0.22 \pm 0.013 = (0.194, 0.246) \]

For Country C, the sample proportion is \(\hat{p} = 0.27\) and the sample size is \(n = 999\).

Again, using the confidence interval formula:

\[ \hat{p} \pm z \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}} \]

Calculating the margin of error:

\[ \text{Margin of Error} = 1.96 \cdot \sqrt{\frac{0.27(1 - 0.27)}{999}} \approx 0.014 \]

Thus, the confidence interval is:

\[ 0.27 \pm 0.014 = (0.242, 0.298) \]

Final Answer