Question

An epidemiologist plans to conduct a survey to estimate the percentage of women who give birth. How many women must be surveyed in order to be 99% confident that the estimated percentage is in error by no more than three percentage points?

Assume that a prior study conducted by an organization showed that 83​% of women give birth.

Answer 1

The epidemiologist would need to survey at least 2750 women to be 99% confident that the estimated percentage is in error by no more than three percentage points.

Step-by-step explanation:

To estimate the required sample size, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

n = required sample size

Z = Z-score corresponding to the desired level of confidence

p = estimated proportion from the prior study

E = maximum allowable error

In this case, the desired level of confidence is 99%, p is 0.83, and E is 0.03. The Z-score is found from the standard normal distribution table for a 99% confidence level, which is approximately 2.576.

Substituting the values into the formula:

n = (2.576^2 * 0.83 * (1-0.83)) / 0.03^2

n = (6.651 * 0.83 * 0.17) / 0.0009

n ≈ 2,749.87

Rounding up to the nearest whole number, the epidemiologist would need to survey at least 2750 women to be 99% confident that the estimated percentage is in error by no more than three percentage points.