Question

In a sample of 280 adults, 258 had children. Construct a 99% confidence interval for the true population proportion of adults with children. Give your answers as decimals, to three places ________ < p < ________

Answer 1

To construct a 99% confidence interval for the true population proportion of adults with children, divide the number of adults with children by the total number of adults to get the sample proportion. Therefore, the 99% confidence interval for the true population proportion of adults with children is approximately 0.893 < p < 0.949.

Step-by-step explanation:

To construct a confidence interval for the true population proportion of adults with children, we can use the formula:

p' ± EBP

Where p' is the sample proportion and EBP is the error bound.

First, calculate the sample proportion:

p' = number of adults with children / total number of adults

p' = 258 / 280

p' ≈ 0.921

Next, calculate the error bound:

EBP = Z * sqrt((p' * (1 - p')) / n)

Where Z is the z-score corresponding to the confidence level, p' is the sample proportion, and n is the sample size.

For a 99% confidence level, Z is approximately 2.576.

Substituting the values into the formula:

EBP = 2.576 * sqrt((0.921 * (1 - 0.921)) / 280)

EBP ≈ 0.028

Finally, construct the confidence interval:

p' ± EBP

0.921 ± 0.028

Therefore, the 99% confidence interval for the true population proportion of adults with children is approximately 0.893 < p < 0.949.