Question

A sample of 2,047 American adults was asked how they viewed China, with 29% of respondents calling the country "unfriendly" and 9% of respondents indicating the country was "an enemy." Construct a 95% confidence interval of the proportion of American adults who viewed China as either "unfriendly" or "an enemy."

Answer 1

To construct a confidence interval for the proportion of American adults who viewed China as either "unfriendly" or "an enemy," we can use the following formula:

CI = p ± z*(√(p(1-p)/n))

where:

CI is the confidence interval

p is the sample proportion (0.29 + 0.09 = 0.38)

z is the critical value for the desired confidence level (95% confidence level corresponds to z = 1.96)

n is the sample size (2,047)

Plugging in the values, we get:

CI = 0.38 ± 1.96*(√(0.38*(1-0.38)/2047))

CI = 0.38 ± 0.018

CI = (0.362, 0.398)

Therefore, we can say with 95% confidence that the true proportion of American adults who view China as either "unfriendly" or "an enemy" is between 0.362 and 0.398.