Question

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.

Click here to view the standard normal distribution table (page 1)

Click here to view the standard normal distribution table (page 2)

Click here to view the table of critical t-values.

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 ​$__ and ​$__.

Answer 1

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