# PiggyBank- Sample size

PiggyBank wants 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, PiggyBank 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 PiggyBank 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.

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#### Solution Preview

Standard deviation = = $500

confidence interval= 98%

This is a two tailed test since we are checking for both plus or minus $10

Let the true mean be mu ;

What this problem is saying that we should be in the range mu+10 and mu-10 and

With sampling we determine the confidence interval of mu +Z x standard error of mean and mu-Z x standard error of mean

where

Z is read from the normal probability distribution tables corresponding to the confidence interval ...

#### Solution Summary

The sample size for an error of less than plus or minus $10 of the true mean with a 98% confidence level is calculated