Question

Use the given data and degree of confidence to construct the confidence interval that is an estimate of the population proportion p. n = 900, x = 400, 95% confidence

Answer 1

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).