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."

To construct a 95% confidence interval for the proportion of American adults who view China as either "unfriendly" or "an enemy," we first need to calculate the combined proportion and then apply the formula for the confidence interval.

1. **Calculate the combined proportion**:
   - Proportion of "unfriendly": \( p_1 = 0.17 \)
   - Proportion of "an enemy": \( p_2 = 0.06 \)
   - Combined proportion: 
     \[
     p = p_1 + p_2 = 0.17 + 0.06 = 0.23
     \]

2. **Determine the sample size**:
   - \( n = 2007 \)

3. **Calculate the standard error (SE)**:
   \[
   SE = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23 \times (1 - 0.23)}{2007}} = \sqrt{\frac{0.23 \times 0.77}{2007}} \approx \sqrt{\frac{0.1771}{2007}} \approx \sqrt{0.0000882} \approx 0.0094
   \]

4. **Determine the Z-score for a 95% confidence level**:
   - The Z-score for a 95% confidence interval is approximately 1.96.

5. **Calculate the margin of error (ME)**:
   \[
   ME = Z \times SE = 1.96 \times 0.0094 \approx 0.0184
   \]

6. **Construct the confidence interval**:
   - Lower limit: 
     \[
     p - ME = 0.23 - 0.0184 \approx 0.2116
     \]
   - Upper limit: 
     \[
     p + ME = 0.23 + 0.0184 \approx 0.2484
     \]

Thus, the 95% confidence interval for the proportion of American adults who view China as either "unfriendly" or "an enemy" is approximately **(0.2116, 0.2484)**.

### Summary
- **95% Confidence Interval**: (0.2116, 0.2484)

Would you like further details or clarification on any part of this calculation? Here are some related questions you might consider:
1. How do you interpret a confidence interval in practical terms?
2. What would happen to the confidence interval if the sample size were larger?
3. How do you calculate a confidence interval for a single proportion?
4. What assumptions are made when constructing this confidence interval?
5. How can you determine the required sample size for a desired margin of error? 

**Tip**: Always ensure your sample is representative to improve the reliability of your confidence intervals.

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.'

Discover how to construct a 95% confidence interval for the proportion of American adults who view China as either 'unfriendly' (17%) or 'an enemy' (6%). This step-by-step guide uses a sample size of 2,007 to calculate the interval as approximately (0.2116, 0.2484).

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