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# Confidence interval for a population mean

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A finance company needs to estimate the mean number of credit cards held by an American family. From past experience, the company knows that the standard deviation of the population is 1.16 cards. The company takes a random sample of n=31 families and finds the sample mean number of cards to be 4.6. Use this data to find a 90% confidence interval for u or mu.

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Please see the attached MS Word document.

A 90% Confidence interval can be calculated as follows:

Where is the (1- )100th Percentile of a standard normal distribution.

In this particular case, it's the 95th percentile, since we want a 90% confidence interval. From the standard normal tables it can be found to be 1.645.

Lower end point of interval =

The upper end point of the interval =

You can be 90% confident that the true value of the population mean lies between the two endpoints of this interval.

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