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 (□,□) (round to three decimal places as needed.)

Explanation:

Step1: Calculate the standard error

The formula for the standard error \(SE\) of a proportion is \(SE=\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\), where \(\hat{p}\) is the sample proportion and \(n\) is the sample size.
For Country A, \(\hat{p}=0.33\) and \(n = 1008\).

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Step2: Find the margin of error

For a 95% confidence interval, the critical value \(z\) is \(z = 1.96\).
The margin of error \(ME=z\times SE\).

$$ ME=1.96\times0.0148\approx0.0290 $$

Step3: Calculate the confidence interval

The confidence interval for a proportion is \(\hat{p}-ME

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Answer:

\((0.301,0.359)\)