Question

the figure to the right shows the results of a survey in which 1010 adults from country a, 1012 adults from country b, 1002 adults from country c, 996 adults from country d, and the 95% confidence interval for the proportion of adults from country a who say national identity is strongly tied to birthplace is (0.291, 0.349) (round to three decimal places as needed.) the 95% confidence interval for the proportion of adults from country b who say national identity is strongly tied to birthplace is (□□) (round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion and sample size for Country B

The sample proportion \( \hat{p} = 0.20\) (since \(20\%=0.20\)), and the sample size \(n = 1012\).

Step2: Calculate the standard error

The formula for the standard error of a proportion is \(SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\).
Substitute \(\hat{p}=0.20\) and \(n = 1012\) into the formula:

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Step3: Find the critical value

For a 95% confidence interval, the critical value \(z\) (using the standard normal distribution) is \(z = 1.96\).

Step4: Calculate the margin of error

The margin of error \(ME=z\times SE\).
Substitute \(z = 1.96\) and \(SE\approx0.0126\) into the formula:
\(ME=1.96\times0.0126\approx0.0247\)

Step5: Calculate the confidence interval

The confidence interval is \(\hat{p}-MESubstitute \(\hat{p}=0.20\) and \(ME\approx0.0247\) into the formula:
\(0.20- 0.0247=0.175\) and \(0.20 + 0.0247=0.225\)

Answer:

\((0.175,0.225)\)