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# PiggyBank- Sample size

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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.

https://brainmass.com/statistics/confidence-interval/piggybank-sample-size-32577

#### 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

\$2.49