Question

In a random sample of 81 audited estate tax returns, it was determined that the mean amount of additional tax owed was $442 wth a standard deviation of 2554. Construct and intepasos conocer mean additional amount of tax owed for estate tax returns. Click here to view the standard normal distribution tabletage 1). Click here to view the standard normal distrution table (page 21 Click here to view the table of critical values Find and interpreta 90% confidence interval for the mean additional amount of tax owed for state tax retums. Select the correct choice below and in the answer boves to compete your choice (Use ascending order. Round to the nearest dollar as needed) O A There is a 90% probability that the mean additional tax owed is between $ and s OB. 90% of taxes owed for state tax returns are between $ and $ OC One can be 90% confident that the mean additional tax owed is between $ ands

Answer 1

Solution:

The 90% confidence interval is given by,

$C.I.=\begin{pmatrix} \bar{x}-Z_{\alpha /2}\frac{\sigma }{\sqrt{n}},\bar{x}+Z_{\alpha /2}\frac{\sigma }{\sqrt{n}} \end{pmatrix}$

$C.I.=\begin{pmatrix} 3442-1.645\frac{2554}{\sqrt{81}},3442+1.645\frac{2554}{\sqrt{81}} \end{pmatrix}$

C.I. = (2975.227,3908.773)

$C.I.=(2975,3909)$

Option (C) is correct.

One can be confident that the mean additional tax owed is between $2975 and $3909.

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