Question

For the purposes of managing disposable cup inventory, a coffee shop wishes to estimate the proportion of customers who bring their own reusable cup for beverage purchases. They want their estimate to be accurate to within 4.5 percentage points with 95% confidence. How many beverage purchases should they randomly select to accomplish this?

(A) 334
(B) 335
(C) 22
(D) 474
(E) 475

Answer 1

To estimate the proportion of customers who bring their own reusable cup, the coffee shop should randomly select 385 beverage purchases with a 95% confidence level and a margin of error of 4.5 percentage points.

Step-by-step explanation:

To estimate the proportion of customers who bring their own reusable cup with a 95% confidence level and a margin of error of 4.5 percentage points, we need to calculate the sample size. The formula for sample size is:

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

Where Z is the z-score corresponding to the desired confidence level (95% = 1.96), p is the estimated proportion (0.5 for maximum sample size), and E is the margin of error (0.045).

Substituting the values into the formula:

Sample Size = (1.96^2 * 0.5 * (1-0.5)) / (0.045^2) = 384.756 ≈ 385

Therefore, the coffee shop should randomly select 385 beverage purchases in order to estimate the proportion of customers who bring their own reusable cup.