# Assuming that the population standard deviation of the additional amount owed is \$2,583, construct and interpret a 99% confidence interval for the meaIn a random sample of 100 estate tax returns...

Assuming that the population standard deviation of the additional amount owed is \$2,583, construct and interpret a 99% confidence interval for the mea

In a random sample of 100 estate tax returns that was audited by the Internal Revenue Service, it was determined that the mean amount of additional tax owed was \$3,421.  Assuming that the population standard deviation of the additional amount owed is \$2,583, construct and interpret a 99% confidence interval for the mean additional amount of tax owed for estate tax returns.

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We are given `bar(x)=3421,sigma=2583,n=100,alpha=.01` . Since we know the population standard deviation, we can use the z distribution.

Then `bar(x)-z_(alpha/2)(sigma/sqrt(n))<=mu<=bar(x)+z_(alpha/2)(sigma/sqrt(n))`

`alpha/2=.005` , and using a standard normal table we get `z_(.005)=2.58`

`3421-2.58(2583/sqrt(100))<=mu<=3421+2.58(2583/sqrt(100))`

`2754<=mu<=4087`

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We can be 99% certain that the mean of the additional amount of taxes owed is in the interval `\$2754<=mu<=\$4087`

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