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# Sample Size and Confidence Intervals

See the attached file.

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 \$55 of the true mean with a 95% confidence level. The standard deviation is thought to be \$700. How many card holders should be sampled? Your company charges a set dollar amount for each account in the sample.

After you've determined how many card holders should be sampled, Universal Credit Inc. comes back and says the cost for the analysis is greater than their budget for the project and they want you to lower the sample size.

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 decrease the sample to meet their budget.

#### Solution Preview

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 \$55 of the true mean with a 95% confidence level. The standard deviation is thought to be \$700. How many card holders should be sampled? Your company charges a set dollar amount for each account in the sample.

To do this, we need to use the formula for a 95% confidence interval for a mean. The formula is the following (reference: http://www.mathwizz.com/statistics/help/help7.htm):

We can plug the following values into the formula:

x = unknown (the ...

#### Solution Summary

This solution uses calculations for confidence interval of the mean in order to determine the minimum number of people to be sampled. A discussion regarding what would happen if the sample size is decreased is then given.

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