A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 99% confidence?

Question

Quizplus · Accepted Answer

We use the formula n = (z^2 * p * q) / E^2, where z = 2.576 (from the z-table for 99% confidence), p = 0.4, q = 0.6, and E = 0.03. Plugging in the values, we get n = (2.576^2 * 0.4 * 0.6) / 0.03^2 = 1775.745. Since we need a whole number for the sample size, we round up to 1776. Therefore, choice C is the best option.

A Report States That 40% of Home Owners Had a Vegetable