Universal Credit: How Many Cardholders Should Be Sampled?
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A partner company to American Intellectual Union (AIU), Universal Credit Inc., would like to examine the required sample size needed to be able to estimate the mean dollars that each card holder will spend each month. It would like to be within plus or minus $10 of the true mean with a 98% confidence level. The standard deviation is thought to be $500. How many card holders should be sampled?
After you've determined how many card holders should be sampled, Universal Credit Inc. comes back and says that it will cost $5 per sample, and they were only planning on spending $10,000 on the sample.
In a memo to the Universal Credit product development team, indicate how many card holders should be sampled to meet the original requirements of the sample.
Then explain the trade-offs that will occur when you lower the sample to $10,000 to meet their budget.
Please list any references or web sources for citation.
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Solution Summary
The solution determines how many cardholders should be sampled.
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The formula to determine the required sample size to attain a target margin of error is as follows:
N = [z(alpha/2) * sigma/E]^2
where
alpha is the significance level (since the confidence level is 98% in this case, then the significance level is 0.02 - so alpha/2 is 0.01)
z(alpha/2) is the critical value of the normal distribution that leaves a probability alpha/2 at its right
sigma is the standard deviation of the population (in your case, 500)
E is the margin of error (in your case, 10, because the problem statement says "It would like to be within plus or minus $10 of the true mean...")
[The above formula can be ...
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