Question

Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using alpha equals0.05 . Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice​ salaries? Based on the​ results, does it appear that justices might profit by levying larger​ fines? Court Income 64.0 405.0 1567.0 1132.0 270.0 252.0 110.0 150.0 32.0 Justice Salary 29 43 91 55 44 61 26 27 18 What are the null and alternative​ hypotheses? A. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho less than 0 B. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho not equals 0 C. Upper H 0 ​: rho equals 0 Upper H 1 ​: rho greater than 0 D. Upper H 0 ​: rho not equals 0 Upper H 1 ​: rho equals 0 Construct a scatterplot. Choose the correct graph below. A. 08001600 050100Court IncomeJustice Salary A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (140, 14); (140, 36); (340, 42); (660, 54); (740, 66); (900, 74); (1280, 90); (1320, 14); (1420, 74). B. 08001600 050100Court IncomeJustice Salary A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (40, 18); (60, 30); (120, 26); (160, 28); (260, 62); (280, 44); (400, 44); (1140, 56); (1560, 92). C. 08001600 050100Court IncomeJustice Salary A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (260, 84); (420, 24); (640, 56); (760, 86); (880, 48); (900, 34); (1040, 86); (1260, 46); (1480, 18). D. 08001600 050100Court IncomeJustice Salary A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (220, 84); (220, 80); (360, 80); (400, 70); (580, 84); (740, 58); (1080, 62); (1120, 30); (1420, 44). The linear correlation coefficient r is nothing . ​(Round to three decimal places as​ needed.) The test statistic t is nothing . ​(Round to three decimal places as​ needed.) The​ P-value is nothing . ​(Round to three decimal places as​ needed.) Because the​ P-value is ▼ greater less than the significance level 0.05 ​, there ▼ is not is sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of alpha equals0.05 . Based on the​ results, does it appear that justices might profit by levying larger​ fines? A. It does appear that justices might profit by issuing smaller fines. B. It does not appear that justices might profit by levying larger fines. C. It does appear that justices might profit by levying larger fines. D. It appears that justices profit the same despite the amount of the fines. Click to select your answer(s).

Answer 1

NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha:

alpha=0.05

SCATTER PLOT OPTION B

r= 0.864

test statistic t= r*sqrt(n-2)/sqrt(1-r^2)= 0.864*sqrt(9-2)/sqrt(1-(0.864)^2) = 0.864*2.65/0.503 = 4.552

p value= 0.003

Because the​ P-value is less than the significance level 0.05 ​, there is sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of alpha equals =0.05

It appears that justices profit the same despite the amount of the fines