Question

# In a random sample of 81 audited estate tax​ returns, it was determined that the mean...

In a random sample of 81 audited estate tax​ returns, it was determined that the mean amount of additional tax owed was ​\$3477 with a standard deviation of ​\$2512. Construct and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns.

Find and interpret a​ 90% confidence interval for the mean additional amount of tax owed for estate tax returns. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Use ascending order. Round to the nearest dollar as​ needed.)

A. One can be​ 90% confident that the mean additional tax owed is between ​\$__ and ​\$__.

B. ​90% of taxes owed for estate tax returns are between ​\$__and ​\$__.

C. There is a​ 90% probability that the mean additional tax owed is between ​\$__ and ​\$__.

Solution:
Given that, n=81 ,x̄=​\$3477,S= \$2512.
(1–α)%=90%
α=0.10
α/2=0.05
t(α/2),(n-1)=t(0.05),(,80)
= 1.664 ....from student t table.
Margin of error=E=t(α/2),(n-1)×(S/✓n)
=1.664 ×(2512/✓81)
= 464.4409
Margin of error=E=464.4409
90% confidence interval for true population mean μ given as,
x̄± Margin of error=( 3477̄± 464.4409)
=(3012.5591,3941.4409)
=(\$3013,\$3941) ... Nearest dollar

A)
One can be 90% confident that the mean additional tax owed is between ​\$3013 and ​\$3941

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