You want to create a 99% confidence interval with a margin of error of 5. Assuming the population standard deviation is equal to 1.5, what's the minimum size of the random sample you can use for this purpose?
A. 59
B. 58
C. 8
D. 60
E. 7
The formula for calculating the minimum sample size needed for a confidence interval with a given margin of error is:
n = (Z^2 * σ^2) / E^2
Where:
n = sample size
Z = Z-score for the desired confidence level (for 99% confidence, Z = 2.576)
σ = population standard deviation
E = margin of error
Plugging in the values, we get:
n = (2.576^2 * 1.5^2) / 5^2
n = (6.635776 * 2.25) / 25
n = 14.931
n ≈ 15
Therefore, the minimum size of the random sample you can use is 15, so none of the provided options are correct.