Piggy Bank would like to examine the required sample size needed to be able to estimate the meandollars 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 deviationis 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.

The sample size formula is:

n = (z*sigma/m)^2

where sigma is the population standard deviation and

m is the desired margin of error and

n is the necessary sample size

The population standard deviation is 500 ——– given already in problem …

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