Question

widows a recent study indicated that 39% of the 107 women over age 55 in the study were widows. round up your answers to the next whole number for the following questions.
part: 0 / 2
part 1 of 2
how large a sample must you take to be 99% confident that the estimate is within 0.02 of the true proportion of women over age 55 who are widows?
n =

Explanation:

Step1: Identify the formula for sample size

The formula for sample size \(n\) when estimating a proportion is \(n=\frac{z^{2}\cdot p\cdot(1 - p)}{E^{2}}\), where \(z\) is the z - score, \(p\) is the estimated proportion, and \(E\) is the margin of error.
For a \(99\%\) confidence interval, the z - score \(z\) (from the standard normal distribution table) is \(z = 2.576\). The proportion \(p=0.39\) (from the study), and the margin of error \(E = 0.02\).

Step2: Substitute the values into the formula

Substitute \(z = 2.576\), \(p = 0.39\), and \(E=0.02\) into the formula:

$$
LATEXBLOCK0
$$

Step3: Round up the result

Since we need to round up to the next whole number, we consider the value of \(n\).

Answer:

\(n = 3950\)