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 (0.175, 0.225) (round to three decimal places as needed.) the 95% confidence interval for the proportion of adults from country c who say national identity is strongly tied to birthplace is (□,□) (round to three decimal places as needed.)

Explanation:

Step1: Calculate the sample proportion (\(\hat{p}\)) and sample size (\(n\))

For Country C, \(\hat{p}=0.29\), \(n = 1002\)

Step2: Calculate the standard error (\(SE\))

\(SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}=\sqrt{\frac{0.29\times(1 - 0.29)}{1002}}\)
\(=\sqrt{\frac{0.29\times0.71}{1002}}=\sqrt{\frac{0.2059}{1002}}\approx\sqrt{0.0002055}\approx0.0143\)

Step3: Find the critical value (\(z\)) for 95% confidence interval

For 95% confidence interval, \(z = 1.96\)

Step4: Calculate the margin of error (\(ME\))

\(ME=z\times SE=1.96\times0.0143\approx0.0280\)

Step5: Calculate the lower and upper bounds of the confidence interval

Lower bound \(=\hat{p}-ME=0.29 - 0.0280=0.262\)
Upper bound \(=\hat{p}+ME=0.29+0.0280 = 0.318\)

Answer:

\((0.262,0.318)\)