document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #849268 by CPhill(1959)\"\" \"About 
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To determine the sample size needed for this study, we can use the formula for sample size estimation for proportions:\r
\n" ); document.write( "\n" ); document.write( "n = (Z^2 * p * (1-p)) / E^2\r
\n" ); document.write( "\n" ); document.write( "Where:\r
\n" ); document.write( "\n" ); document.write( "* n = sample size
\n" ); document.write( "* Z = Z-score corresponding to the desired confidence level (we'll assume a 95% confidence level, which gives a Z-score of 1.96)
\n" ); document.write( "* 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)
\n" ); document.write( "* E = margin of error (0.015, or 1.5%)\r
\n" ); document.write( "\n" ); document.write( "Let's plug in the values:\r
\n" ); document.write( "\n" ); document.write( "n = (1.96^2 * 0.5 * (1 - 0.5)) / 0.015^2
\n" ); document.write( "n = (3.8416 * 0.25) / 0.000225
\n" ); document.write( "n = 0.9604 / 0.000225
\n" ); document.write( "n ≈ 4268.44\r
\n" ); document.write( "\n" ); document.write( "Since we can't have a fraction of a customer, we always round the sample size *up* to the nearest whole number.\r
\n" ); document.write( "\n" ); document.write( "Therefore, Nice App Inc. would need to survey at least **4269** customers.
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