Answer: We can use the formula for sample size calculation for estimating a population proportion:
n = (z^2 * p * (1 - p)) / E^2
where:
z = the z-score corresponding to the desired level of confidence
p = the estimated proportion from the population (0.13 in this case)
E = the desired margin of error (0.05 in this case)
Substituting the given values, we get:
n = (z^2 * p * (1 - p)) / E^2
n = (2.326^2 * 0.13 * (1 - 0.13)) / 0.05^2
n ≈ 319.8
We need a sample size of at least 320 to be 98% confident that the estimated proportion of women-owned businesses providing profit-sharing and/or stock options is within 5 percentage points of the true population proportion.