A report states that 46% 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 5% with 95%
Confidence?
A)96
B)191
C)382
D)764

Question

Quizplus · Accepted Answer

To find the sample size needed, we can use the formula:
n = (Z^2 * p * q) / E^2
Where:
Z = the Z-score for the desired confidence level (in this case, 1.96 for 95% confidence)
p = the estimated proportion of home owners with vegetable gardens (0.46)
q = 1 - p (0.54)
E = the desired margin of error (0.05)
Plugging in these values, we get:
n = (1.96^2 * 0.46 * 0.54) / 0.05^2
n ≈ 191
Therefore, the best choice is B)191. Using the formula n = (z^2 * p * q) / e^2, we have:

n = (1.96^2 * 0.46 * 0.54) / 0.05^2
n = 191.07

Rounding up to the nearest whole number, we get n = 191. Therefore, a sample of at least 191 home owners is needed to estimate the true proportion of home owners who have vegetable gardens to within 5% with 95% confidence.

A Report States That 46% of Home Owners Had a Vegetable