A report states that 46% of home owners had a vegetable garden. How large a sample is needed to estimate the
A) 96
B) 191
C) 382
D) 764

Question

Quizplus · Accepted Answer

To find the sample size needed to estimate a percentage with a desired margin of error, we use the formula:

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

where:
- n = sample size
- z = z-score based on desired level of confidence (e.g. 1.96 for 95% confidence)
- p = proportion (as a decimal) of the population with the characteristic of interest (in this case, having a vegetable garden)
- q = 1 - p
- E = desired margin of error (as a decimal)

Plugging in the given values, we get:

n = (1.96^2 * 0.46 * 0.54) / (0.03^2)
n = 381.78

Rounding up to the nearest whole number gives us a sample size of 382. This is therefore the best choice, as it provides a 95% confidence level and 3% margin of error for estimating the proportion of home owners with a vegetable garden.

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