Question

Uisted below are amounts of court income and salaries paid to the tewn ustioes All amounts are in uficent evidence to condude that there is a inear conelaion beween court incomes and jualice salaies7 Based on the los appear that justioes might geit by levying lage s Round to thee decimal places as eed The test saistic tin 4853 Round o tree deimal places as needed needed) than the signficance vel 0 05, here Hard to teee deond places ficent evidence to suppot the claim thal there s a linear cio O A. Rappears that junices proft the same despile the amount of the f O D. does appes that untices might profil by issuing smallerfines

Answer 1

@考 X Values

Y Values X Values 65 403 1566 1132 272 252 112 152 32 30 94 58 47 60 24 25 18 0

Х-М (Х-Мх)2 (Y - M,)2 377.889 39.889 1123.111 689.111 170.889 190.889 330.889 290.889 -410.889 -14.444 0.444 49.556 13.556 2.556 15.556 20.444 19.444 -26.444 142800.012 1591.123 1261378.568 474874.123 29203.012 36438.568 109487.457 84616.346 168829.679 208.642 0.198 2455.753 183.753 6.531 241.975 417.975 378.086 699.309 5458.395 17.728 55656. 395 9341.284 436.716 -2969.383 6764.840 5656.173 10865.728 Мх: 442. 889 My 44.444Sum: 2309218.889 Sum 4592.222Sum: 90354.444

X Values Σ = 3986 Mean442.889 2x-Mx)SSx 2309218.889 Y Values :400 Mean = 44.444 ZY-My ssy 4592.222 Xand Y Combined X MxY-My) 90354.444 R Calculation r = 90354444 / v((230921 8.889)(4592.222) 0.8774 Meta Numerics (cross-check) r 0.8774

r = 0.877 (Round to three decimal places)

Test statistic t = r * sqrt( (n-1) / (1-r^2) ) = 4.829

P- value = 0.001881 ~ 0.002

Here

P -value is < 0.05

Reject H0.

Because 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

a-0.05

Based on the results

it does appear that justices might profit by levying larger fines.