Question

Construct a 99% confidence interval to estimate the population proportion with a sample proportion equal to 0.70 and a sample size equal to 200. Click the icon to view a portion of the Cumulative Probabilities for the Standard Normal Distribution table. and an A 99% confidence interval estimates that the population proportion is between a lower limit of upper limit of (Round to three decimal places as needed.)

Answer 1

To construct the 99% confidence interval with the given sample size and proportion, we use the z-score for 99% confidence and find the interval to be between 0.628 and 0.772 after rounding to three decimal places.

Step-by-step explanation:

To construct a 99% confidence interval for estimating a population proportion when the sample proportion is 0.70 and the sample size is 200, we use the formula:

p±z*(sqrt((p*(1-p))/n))

Where p is the sample proportion, z is the z-score for the given confidence level, and n is the sample size.

For a 99% confidence level, the z-score (from the standard normal distribution table) is approximately 2.576. Plugging the values into the formula, we get:

0.70 ± 2.576*(sqrt((0.70*(1-0.70))/200))

This results in a confidence interval of:

(0.70 ± 0.0715)

(0.6285, 0.7715) after rounding to three decimal places.

The 99% confidence interval estimates that the population proportion is between 0.628 and 0.772.