Question

Determine the necessary sample size.

A nutritionist is interested in estimating the proportion of consumers who look to purchase organic produce. How large of a sample would be necessary in order to be 99% confident that the estimate is within 3% of the actual proportion?

(Hint: use a 'worst case scenario' of p=0.50)

Answer 1

To determine the necessary sample size to be 99% confident that the estimate is within 3% of the actual proportion, we can use the formula for sample size calculation.

Step-by-step explanation:

To determine the necessary sample size in order to be 99% confident that the estimate is within 3% of the actual proportion, we can use the formula:

Sample Size = ((Z * Z) * (p * (1 - p))) / (E * E)

Where Z is the Z-score for the desired confidence level (in this case, 99% confidence corresponds to a Z-score of approximately 2.576), p is the estimated proportion (worst-case scenario of 0.50), and E is the desired margin of error (3%).

Substituting the values into the formula:

Sample Size = ((2.576 * 2.576) * (0.50 * (1 - 0.50))) / (0.03 * 0.03) ≈ 752

Therefore, a sample size of 752 would be necessary to be 99% confident that the estimate is within 3% of the actual proportion.