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Develop a 95% confidence interval for the amount of total itemized deductions fo

ID: 3054105 • Letter: D

Question

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?
SelectYes, because the deduction is larger than expectedYes, because the deduction is expectedNo, because the deduction is lower than expectedItem 5

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.

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?
SelectYes, because the deduction is larger than expectedYes, because the deduction is expectedNo, because the deduction is lower than expectedItem 5

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.

Explanation / Answer

Result:

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.

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).
$ ( 11800 , 14490 )

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).
$ (9372  ,  16919)

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?
Yes, because the deduction is larger than expected


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 $16919  could suggest an audit.

Regression Analysis

0.955

n

7

r

0.977

k

1

Std. Error

1.372

Dep. Var.

Reasonable Amount of Itemized Deductions

ANOVA table

Source

SS

df

MS

F

p-value

Regression

199.0083

1  

199.0083

105.79

.0001

Residual

9.4060

5  

1.8812

Total

208.4143

6  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=5)

p-value

95% lower

95% upper

Intercept

4.6768

1.0334

4.526

.0063

2.0203

7.3332

Adusted Gross Income

0.1613

0.0157

10.285

.0001

0.1210

0.2016

Predicted values for: Reasonable Amount of Itemized Deductions

95% Confidence Interval

95% Prediction Interval

Adusted Gross Income

Predicted

lower

upper

lower

upper

Leverage

52.5

13.1455

11.8006

14.4904

9.3720

16.9191

0.146

Regression Analysis

0.955

n

7

r

0.977

k

1

Std. Error

1.372

Dep. Var.

Reasonable Amount of Itemized Deductions

ANOVA table

Source

SS

df

MS

F

p-value

Regression

199.0083

1  

199.0083

105.79

.0001

Residual

9.4060

5  

1.8812

Total

208.4143

6  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=5)

p-value

95% lower

95% upper

Intercept

4.6768

1.0334

4.526

.0063

2.0203

7.3332

Adusted Gross Income

0.1613

0.0157

10.285

.0001

0.1210

0.2016

Predicted values for: Reasonable Amount of Itemized Deductions

95% Confidence Interval

95% Prediction Interval

Adusted Gross Income

Predicted

lower

upper

lower

upper

Leverage

52.5

13.1455

11.8006

14.4904

9.3720

16.9191

0.146

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