Questions: The figure to the right shows the results of a survey in which 1000 adults from Country A, 1005 adults from Country B, 1019 adults from Country C, 996 adults from Country D, and 997 adults from County 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 30% Country B 22% Country C 25% Country D 54% Country E 13% Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. The 99% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is (0.263,0.337). (Round to three decimal places as needed.) The 99% confidence interval for the proportion of adults from County B who say national identity is strongly tied to birthplace is (0.186,0.254). (Round to three decimal places as needed.) The 99% confidence interval for the proportion of adults from County C who say national identity is strongly tied to birthplace is (0.215,0.285). (Round to three decimal places as needed.)

The figure to the right shows the results of a survey in which 1000 adults from Country A, 1005 adults from Country B, 1019 adults from Country C, 996 adults from Country D, and 997 adults from County 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 30% Country B 22% Country C 25% Country D 54% Country E 13% Construct a 99% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. The 99% confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is (0.263,0.337). (Round to three decimal places as needed.) The 99% confidence interval for the proportion of adults from County B who say national identity is strongly tied to birthplace is (0.186,0.254). (Round to three decimal places as needed.) The 99% confidence interval for the proportion of adults from County C who say national identity is strongly tied to birthplace is (0.215,0.285). (Round to three decimal places as needed.)
Transcript text: The figure to the right shows the results of a survey in which 1000 adults from Country A, 1005 adults from Country B, 1019 adults from Country C, 996 adults from Country D, and 997 adults from County E were asked whether national identity is strongly tied to birthplace. \begin{tabular}{|l|} \hline National Identity and Birthplace \\ People from different countries who believe national \\ identity is strongly tied to birthplace \\ \begin{tabular}{|lr|} \hline Country A & $30 \%$ \\ \hline Country B & $22 \%$ \\ \hline Country C & $25 \%$ \\ \hline Country D & $54 \%$ \\ \hline Country E & $13 \%$ \\ \hline \end{tabular} \end{tabular} Construct a $99 \%$ confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. The $99 \%$ confidence interval for the proportion of adults from Country A who say national identity is strongly tied to birthplace is ($0.263,0.337$). (Round to three decimal places as needed.) The $99 \%$ confidence interval for the proportion of adults from County B who say national identity is strongly tied to birthplace is ($0.186,0.254$). (Round to three decimal places as needed.) The $99 \%$ confidence interval for the proportion of adults from County C who say national identity is strongly tied to birthplace is ($0.215,0.285$). (Round to three decimal places as needed.)
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Solution

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Solution Steps

Step 1: Confidence Interval for Country A

To calculate the 99% confidence interval for the proportion of adults from Country A who believe national identity is strongly tied to birthplace, we use the formula:

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

Where:

  • \(\hat{p} = 0.30\)
  • \(n = 1000\)
  • \(z \approx 2.576\) (for 99% confidence level)

Calculating the margin of error:

\[ \text{Margin of Error} = 2.576 \cdot \sqrt{\frac{0.30(1 - 0.30)}{1000}} \approx 0.037 \]

Thus, the confidence interval is:

\[ 0.30 \pm 0.037 = (0.263, 0.337) \]

Step 2: Confidence Interval for Country B

For Country B, we apply the same formula:

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

Where:

  • \(\hat{p} = 0.22\)
  • \(n = 1005\)

Calculating the margin of error:

\[ \text{Margin of Error} = 2.576 \cdot \sqrt{\frac{0.22(1 - 0.22)}{1005}} \approx 0.034 \]

Thus, the confidence interval is:

\[ 0.22 \pm 0.034 = (0.186, 0.254) \]

Step 3: Confidence Interval for Country C

For Country C, we again use the same formula:

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

Where:

  • \(\hat{p} = 0.25\)
  • \(n = 1019\)

Calculating the margin of error:

\[ \text{Margin of Error} = 2.576 \cdot \sqrt{\frac{0.25(1 - 0.25)}{1019}} \approx 0.035 \]

Thus, the confidence interval is:

\[ 0.25 \pm 0.035 = (0.215, 0.285) \]

Final Answer

The 99% confidence intervals for the proportions of adults who believe national identity is strongly tied to birthplace are as follows:

  • Country A: \((0.263, 0.337)\)
  • Country B: \((0.186, 0.254)\)
  • Country C: \((0.215, 0.285)\)

\[ \boxed{ \begin{align_} \text{Country A:} & \ (0.263, 0.337) \\ \text{Country B:} & \ (0.186, 0.254) \\ \text{Country C:} & \ (0.215, 0.285) \end{align_} } \]

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