A sample of 2,007 American adults was asked how they viewed China, with 17% of respondents calling the country "unfriendly" and 6% 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."
A) [0.2013, 0.2587]
B) [0.2116, 0.2484]
C) [0.2146, 0.2454]
D) [0.2208, 0.2392]

Question

Quizplus · Accepted Answer

The proportion of American adults who viewed China as either "unfriendly" or "an enemy" is calculated as the sum of the proportions who called China "unfriendly" and "an enemy." Thus, the sample proportion is (0.17 + 0.06) = 0.23.

To calculate the 95% confidence interval, we can use the formula:

sample proportion ± (critical value) * (standard error)

where the critical value can be found using a standard normal distribution table or calculator and the standard error is given by:

sqrt((p * q) / n)

where p is the proportion of interest (0.23), q is the complement of p (1 - p = 0.77), and n is the sample size (2,007).

Using a standard normal distribution table or calculator, the critical value for a 95% confidence interval is approximately 1.96.

Plugging in the values, we get:

0.23 ± (1.96) * sqrt((0.23 * 0.77) / 2,007)

Simplifying, we get:

0.23 ± 0.018

Therefore, the 95% confidence interval is [0.2116, 0.2484].

A Sample of 2,007 American Adults Was Asked How They