In: Statistics and Probability
Data are given below on the adjusted gross income x and
the amount of itemized deductions...
Data are given below on the adjusted gross income x and
the amount of itemized deductions taken by taxpayers. Data were
reported in thousands of dollars. With the estimated regression
equation = 4.68 + .16x, the point estimate of a
reasonable level of total itemized deductions for a taxpayer with
an adjusted gross income of $52.5 thousand is $13.08
thousand.
Adjusted Gross Income ($1000s) |
Reasonable Amount of
Itemized Deductions ($1000s) |
22 |
|
9.6 |
|
27 |
|
9.6 |
|
32 |
|
10.1 |
|
48 |
|
11.1 |
|
65 |
|
13.5 |
|
85 |
|
17.7 |
|
120 |
|
25.5 |
|
In the questions that follow, enter the dollar amounts requested.
For example, if the regression results provide a value of 11.74
thousand, enter 11,740 as the dollar amount in the box. Use Table 1
of Appendix B.
- Develop a 95% confidence interval for the amount of total
itemized deductions for all taxpayers with an adjusted gross income
of $52,500 (to the nearest whole number).
$ ( , )
- Develop a 95% prediction interval for the amount of total
itemized deductions for a particular taxpayer with an adjusted
gross income of $52,500 (to the nearest whole number).
$ ( , )
- If the particular taxpayer referred to in part (b) claimed
total itemized deductions of $20,400, would the IRS agent's request
for an audit appear to be justified?
- Use your answer to part (b) to give the IRS agent a guideline
as to the amount of itemized deductions that would suggest an audit
for a taxpayer with an adjusted gross income of $52,500.
Any deductions exceeding the upper limit of
$ could suggest an audit.