Final answer:
To calculate the confidence interval for a population proportion, we can use the formula: p' ± EBP. In this case, we have a sample size of 900, with 400 successes and a 95% confidence level. Using the formula, the 95% confidence interval for the population proportion p is (0.417, 0.471).
Step-by-step explanation:
To calculate the confidence interval for a population proportion, we can use the formula:
p' ± EBP
where p' is the sample proportion (x/n), EBP is the margin of error, and n is the sample size. The margin of error can be calculated using the formula:
EBP = Z * √((p' * (1-p')) / n)
where Z is the Z-score corresponding to the desired level of confidence. In this case, we have n = 900, x = 400, and a 95% confidence level. Computing the values, we have p' = 400/900 = 0.444, q' = 1 - p' = 0.556, and Z = 1.96 (for a 95% confidence level).
Now we can calculate the EBP:
EBP = 1.96 * √((0.444 * 0.556) / 900) = 0.027
Finally, we can construct the confidence interval:
p' ± EBP = 0.444 ± 0.027
Therefore, the 95% confidence interval for the population proportion p is (0.417, 0.471).