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
national identity and birthplace
people from different countries who believe national identity is strongly tied to birthplace
country a 32%
country b 20%
country c 29%
country d 52%
country e 14%
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 (0.262, 0.318). (round to three decimal places as needed.)
the 95% confidence interval for the proportion of adults from country d who say national identity is strongly tied to birthplace is (0.489, 0.551). (round to three decimal places as needed.)
the 95% confidence interval for the proportion of adults from country e who say national identity is strongly tied to birthplace is (□□). (round to three decimal places as needed.)

Explanation:

Step1: Calculate margin of error formula

The formula for a confidence interval for a proportion is $\hat{p}\pm E$, where $\hat{p}$ is the sample proportion and $E$ is the margin of error. For a proportion, $E = z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$. For a 95% confidence interval, $z = 1.96$.
For Country E, $\hat{p}=0.14$ and $n = 996$.
First, calculate $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}=\sqrt{\frac{0.14\times(1 - 0.14)}{996}}=\sqrt{\frac{0.14\times0.86}{996}}=\sqrt{\frac{0.1204}{996}}\approx\sqrt{0.000121}\approx0.011$.
Then, $E=1.96\times0.011 = 0.022$.

Step2: Calculate lower and upper bounds

The lower bound is $\hat{p}-E=0.14 - 0.022=0.118$.
The upper bound is $\hat{p}+E=0.14 + 0.022=0.162$.

Answer:

$(0.118,0.162)$