Question

The Transactional Records Access Clearinghouse at Syracuse University reported data showing the odds of an Internal Revenue Service audit. The following table shows the average adjusted gross income reported (in dollars) and the percent of the returns that were audited for 20 selected IRS districts.

District	Adjusted Gross Income ($)	Percent Audited
Los Angeles	36,664	1.3
Sacramento	38,845	1.1
Atlanta	34,886	1.1
Boise	32,512	1.1
Dallas	34,531	1.0
Providence	35,995	1.0
San Jose	37,799	0.9
Cheyenne	33,876	0.9
Fargo	30,513	0.9
New Orleans	30,174	0.9
Oklahoma City	30,060	0.8
Houston	37,153	0.8
Portland	34,918	0.7
Phoenix	33,291	0.7
Augusta	31,504	0.7
Albuquerque	29,199	0.6
Greensboro	33,072	0.6
Columbia	30,859	0.5
Nashville	32,566	0.5
Buffalo	34,296	0.5

(a) Develop the estimated regression equation that could be used to predict the percent audited given the average adjusted gross income reported (in dollars). (Round your value for the y-intercept to three decimal places and your value for the slope to six decimal places.)

ŷ =  

(b)At the 0.05 level of significance, determine whether the adjusted gross income (in dollars) and the percent audited are related. (Use the F test.)

State the null and alternative hypotheses.

a)H₀: β₁ = 0
H_a: β₁ ≠ 0

B)H₀: β₀ ≠ 0
H_a: β₀ = 0     

C)H₀: β₀ = 0
H_a: β₀ ≠ 0

D)H₀: β₁ ≥ 0
H_a: β₁ < 0

E)H₀: β₁ ≠ 0
H_a: β₁ = 0

Find the value of the test statistic. (Round your answer to two decimal places.)

test statistic=

Find the p-value. (Round your answer to three decimal places.)

p-value =

State your conclusion.

A)Do not reject H₀. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.

B)Reject H₀. We cannot conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.     

C)Do not reject H₀. We cannot conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant

D)Reject H₀. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.

c)Did the estimated regression equation provide a good fit? Explain. (Round your answer to three decimal places.)

Since

r² = _______is  _______ (less than 0.55 / at least 0.55), the estimated regression equation  _______( provided / did not provide a good fit)

(d) Use the estimated regression equation developed in part (a) to calculate a 95% confidence interval for the expected percent audited for districts with an average adjusted gross income of $38,000. (Round your answers to two decimal places.)

_______% to _______%

Answer 1

Applying regression on above data:

a)

ŷ = -0.471+0.000039*x

b)

a)H₀: β₁ = 0
H_a: β₁ ≠ 0

value of the test statistic =2.23

p-value =0.038

D)Reject H₀. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.

c)

r² =0.2171 is less than 0.55  the estimated regression equation did not provide

d)

95% confidence interval for the expected percent audited =0.81 , 1.19

(please try 0.52 ,1.48 if this comes wrong)