In: Statistics and Probability
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.
H0: β1 ≠ 0
Ha: β1 = 0
H0: β1 ≥ 0
Ha: β1 <
0
H0: β0 = 0
Ha: β0 ≠ 0
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 = 0
Ha: β1 ≠ 0
Find the value of the test statistic. (Round your answer to two decimal places.)
_______
Find the p-value. (Round your answer to three decimal places.)
p-value = ______
State your conclusion.
Do not reject H0. We cannot conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.
Do not reject H0. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.
Reject H0. We cannot conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.
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 (---Select--- less than 0.55 at least 0.55) , the estimated regression equation (---Select--- 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 $35,000. (Round your answers to two decimal places.)
_____% to _____%