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 6% with 98%
Confidence?

Question

Quizplus · Accepted Answer

To calculate the sample size, we use the formula:

n = (Z^2 * p * q) / E^2

where:
Z = the critical value for the confidence level = 2.33 (from the Z-table for 98% confidence)
p = the estimated proportion of home owners with vegetable gardens = 0.40
q = the complement of p = 0.60
E = the maximum error of estimate = 0.06

Substituting the values, we get:

n = (2.33^2 * 0.40 * 0.60) / 0.06^2
n = 212.96

Rounding up to the nearest whole number, we get:

n = 213

Therefore, the best choice is C.

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