Final answer:
The margin of error for a 93% confidence interval regarding American adults' approval of stronger laws to reduce greenhouse gas emissions is calculated using the formula E = Z*(√p*(1-p)/n) with the Z-score for 93%, the sample proportion, and the sample size.
Step-by-step explanation:
To find the margin of error for a 93% confidence interval used to estimate the population proportion, we use the formula for the margin of error in a proportion:
E = Z*(√p*(1-p)/n)
Where E is the margin of error, Z is the Z-score corresponding to the confidence level, p is the sample proportion, and n is the sample size.
First, we determine the sample proportion (p) by dividing the number of respondents who approve (1249) by the total number of respondents (1692).
Next, we find the Z-score for a 93% confidence interval, which can be obtained from a Z-score table or calculator.
- Z ≈ 1.81 (Using a standard Z-score table for a 93% confidence interval)
Compute the margin of error (E) using the sample proportion and the Z-score:
- E = 1.81*(√p*(1-p)/1692)
- E = 1.81*(√(1249/1692)*(1-(1249/1692))/1692)
Calculate E and round it off to the appropriate number of decimal places.
The calculated E gives us the margin of error for the 93% confidence interval regarding the proportion of American adults who approve of stronger laws to reduce greenhouse gas emissions.