In a random sample of 64 audited estate tax returns, it was determined that the mean amount of additional tax owed was $3489 with a standard deviation of $2595.
construct and interpret a 90% confidence interval for the mean additional amount of tax owed for estate tax returns.
1) the lower bound is $?
2) the upper bound is $?

Formula for confidence interval for population mean ( if population standard deviation is unknown ) :

, where n= sample size

= sample mean

s= sample standard deviation

= two-tailed t-value for significance level of ().

Let x denotes the amount of additional tax owed .

We assume that amount of additional tax owed is normally distributed .

As per given , we have

n=  64

Degree of freedom : df = 63    [ df= n-1]

s= $2595

Using t-distribution table ,

Then , 90% confidence interval for the mean additional amount of tax owed for estate tax returns would be :

1) The lower bound is $2947.49  .

2) The upper bound is $4030.51  .

Interpretation : We are 90% confident that the true population mean amount of additional tax owed lies between $2947.49 and  $4030.51.

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step-by-step explanation:

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