Answer: To determine the sample size needed for estimating the proportion of consumers who look to purchase organic produce with 99% confidence and a margin of error of 3%, we can use the formula for the sample size of a proportion:
Sample size (n) = (Z^2 * p * q) / E^2
where:
Z = Z-score for the desired level of confidence (in this case, for 99% confidence, Z ≈ 2.576)
p = estimated proportion (use a worst-case scenario of p = 0.50 for maximum sample size)
q = 1 - p
E = margin of error (3% = 0.03)
Now, let's plug in the values:
n = (2.576^2 * 0.50 * 0.50) / 0.03^2
n = (6.633776 * 0.25) / 0.0009
n = 1.658444 / 0.0009
n ≈ 1842.71
Since we cannot have a fraction of a participant, we need to round up to the nearest whole number. Therefore, a sample size of 1843 participants would be necessary to be 99% confident that the estimate of the proportion of consumers who look to purchase organic produce is within 3% of the actual proportion, using a worst-case scenario of p = 0.50.