Question

A retailer wants to estimate with 99% confidence the number of people who shop at his store. A previous study showed that 24% of those interviewed had shopped at his store. He wishes to be accurate within 3% of the true proportion. The minimum sample size necessary would be 1,100.

A. True
B. False

Answer 1

The correct answer is option B. False. To estimate the number of people who shop at his store with 99% confidence and an accuracy of 3%, the retailer would need a larger sample size.

Step-by-step explanation:

To estimate the number of people who shop at his store with 99% confidence and an accuracy of 3%, the retailer would need a larger sample size. The minimum sample size necessary would be calculated using the formula:

n = (Z^2 * p * (1-p))/(E^2)

Where:

• n = sample size
• Z = z-score corresponding to the desired confidence level
• p = estimated proportion
• E = margin of error

In this case, the margin of error is 3% (0.03) and the estimated proportion is 24% (0.24). Plugging in these values, the minimum sample size necessary would be:

n = (2.576^2 * 0.24 * (1-0.24))/(0.03^2) = 1000

Therefore, the statement that the minimum sample size necessary is 1100 is false.