Final answer:
The margin of error for a 90% confidence interval to estimate the population proportion with a sample proportion of 0.36 and sample size of 125 is approximately 0.07. This is calculated by using the standard formula for margin of error in a confidence interval for a population proportion. The closest answer choice to the calculated margin of error is option (B) 0.07.
Step-by-step explanation:
The student has asked to calculate the margin of error for a 90% confidence interval to estimate the population proportion when given a sample proportion (p') of 0.36 and a sample size (n) of 125. The formula for the margin of error in this case is:
EBP = Z * sqrt((p' * (1 - p')) / n)
Where:
- Z is the Z-score corresponding to the desired confidence level, which for a 90% confidence interval is about 1.645.
- p' is the sample proportion, which is given as 0.36.
- n is the sample size, which is given as 125.
Plugging in the values we get:
EBP = 1.645 * sqrt((0.36 * (1 - 0.36)) / 125)
EBP = 1.645 * sqrt(0.2304 / 125)
EBP = 1.645 * sqrt(0.0018432)
EBP = 1.645 * 0.0429269
EBP ≈ 0.0706
The closest answer choice to 0.0706 is (B) 0.07. Therefore, the margin of error for the 90% confidence interval for the population proportion is approximately 0.07, which corresponds to option (B).