Question

the figure to the right shows the results of a survey in which 1008 adults from country a, 1018 adults from country b, 1007 adults from country c, 1019 adults from country d, and 1003 adults from country e were asked whether national identity is strongly tied to birthplace. construct a 95% confidence interval for the population proportion of adults who say national identity is strongly tied to birthplace for each country listed. the 95% confidence interval for the proportion of adults from country a who say national identity is strongly tied to birthplace is (0.301, 0.359). (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: 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, $n$ is the sample size, and for a 95% confidence interval, $z = 1.96$.
For Country B: $\hat{p}=0.19$, $n = 1018$.

Step2: Calculate the margin of error

First, calculate the margin of error $E=z\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}$.
Substitute the values:

$$
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$$

Step3: Calculate the confidence interval

The lower bound is $\hat{p}-E=0.19 - 0.0241=0.166$.
The upper bound is $\hat{p}+E=0.19+0.0241 = 0.214$.

Answer:

$(0.166,0.214)$