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.
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
r²
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
r²
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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