A statistical program is recommended. 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 AdjustedGross Income ($) PercentAudited 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 = −0.471+0.000039x (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: β0 ≠ 0Ha: β0 = 0H0: β1 ≥ 0Ha: β1 < 0 H0: β1 ≠ 0Ha: β1 = 0H0: β1 = 0Ha: β1 ≠ 0H0: β0 = 0Ha: β0 ≠ 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. 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. Do not reject H0. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.Do not reject H0. We cannot 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--- at least 0.55 less than 0.55 , the estimated regression equation ---Select--- did not provide provided 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 $30,000. (Round your answers to two decimal places.) % to %

A statistical program is recommended. 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 AdjustedGross Income ($) PercentAudited 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 = −0.471+0.000039x (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: β0 ≠ 0Ha: β0 = 0H0: β1 ≥ 0Ha: β1 < 0 H0: β1 ≠ 0Ha: β1 = 0H0: β1 = 0Ha: β1 ≠ 0H0: β0 = 0Ha: β0 ≠ 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. 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. Do not reject H0. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.Do not reject H0. We cannot 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--- at least 0.55 less than 0.55 , the estimated regression equation ---Select--- did not provide provided 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 $30,000. (Round your answers to two decimal places.) % to %

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A statistical program is recommended.

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 =

−0.471+0.000039x

(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: β₀ ≠ 0
H_a: β₀ = 0H₀: β₁ ≥ 0
H_a: β₁ < 0 H₀: β₁ ≠ 0
H_a: β₁ = 0H₀: β₁ = 0
H_a: β₁ ≠ 0H₀: β₀ = 0
H_a: β₀ ≠ 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.

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. Do not reject H₀. We conclude that the relationship between the adjusted gross income (in dollars) and the percent audited is significant.Do not reject H₀. We cannot 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--- at least 0.55 less than 0.55 , the estimated regression equation ---Select--- did not provide provided 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 $30,000. (Round your answers to two decimal places.)

% to %

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