# PiggyBank required sample size

Piggy Bank 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, 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

© BrainMass Inc. brainmass.com June 3, 2020, 7:19 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/piggybank-required-sample-size-93401

#### Solution Preview

Hello!

The formula to determine the minimum sample size is:

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 ...

#### Solution Summary

The solution estimates the required sample size for Piggy Bank to estimate the mean spend of each card holder per month for their required confidence levels.