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 (round to three decimal places as needed.)

Explanation:

Step1: Recall the formula for confidence interval

The formula for a confidence interval for a proportion is $\hat{p}\pm z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$, where $\hat{p}$ is the sample proportion, $z$ is the z - score (for a 95% confidence interval, $z = 1.96$), and $n$ is the sample size.
For Country A, $\hat{p}=0.32$ and $n = 1010$.

Step2: Calculate the margin of error

First, calculate $\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}=\sqrt{\frac{0.32\times(1 - 0.32)}{1010}}=\sqrt{\frac{0.32\times0.68}{1010}}=\sqrt{\frac{0.2176}{1010}}\approx\sqrt{0.000215446}\approx0.0147$.
Then, the margin of error $E=z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}=1.96\times0.0147\approx0.029$.

Step3: Calculate the confidence interval

The lower bound is $\hat{p}-E=0.32 - 0.029 = 0.291$.
The upper bound is $\hat{p}+E=0.32+0.029 = 0.349$.

Answer:

$(0.291,0.349)$