Question 1189662: Nice App Inc. wants to provide a special digital reward for users that spend more than $10,000 in the first year of using their new app. In order to estimate how many of the app users will qualify, they decide to perform a study. How many customers would they need to survey to estimate the proportion of users who would qualify for this reward with a 1.5% margin of error?
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! To determine the sample size needed for this study, we can use the formula for sample size estimation for proportions:
n = (Z^2 * p * (1-p)) / E^2
Where:
* n = sample size
* Z = Z-score corresponding to the desired confidence level (we'll assume a 95% confidence level, which gives a Z-score of 1.96)
* p = estimated proportion of users who qualify (since we don't have any prior information, we'll use the most conservative estimate, which is p = 0.5)
* E = margin of error (0.015, or 1.5%)
Let's plug in the values:
n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.015^2
n = (3.8416 * 0.25) / 0.000225
n = 0.9604 / 0.000225
n ≈ 4268.44
Since we can't have a fraction of a customer, we always round the sample size *up* to the nearest whole number.
Therefore, Nice App Inc. would need to survey at least **4269** customers.
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