Step 1 :We are given that we want to be 99% confident, which corresponds to a z-score of 2.576. The margin of error E is 4%, or 0.04. Since we don't know anything about the proportion of adults who gamble online, we'll use the most conservative estimate, which is p = 0.5. This gives us the maximum possible sample size, ensuring that our estimate will be within the desired margin of error.
Step 2 :We use the formula for sample size in a proportion, which is \(n = \frac{Z^2 * p * (1-p)}{E^2}\), where n is the sample size, Z is the z-score, p is the estimated proportion of the population, and E is the desired margin of error.
Step 3 :Substitute the given values into the formula: Z = 2.576, p = 0.5, E = 0.04.
Step 4 :Calculate the sample size, n = 1037.
Step 5 :\(\boxed{1037}\) is the number of adults you must survey in order to be 99% confident that your estimate is in error by no more than four percentage points.