Question

1. Listed below are repair costs (in dollars) for cars crashed at 6 mi/h in full-front crash tests and the same cars crashed at 6 mi/h in full-rear crash tests. The cars are the Toyota Camry, Mazda 6, Volvo S40, Saturn Aura, Subaru Legacy, Hyundai Sonata, and Honda Accord. Is there sufficient evidence to conclude that there is a linear correlation between the repair costs from full-front crashes and full-rear crashes? Front Rear 936 978 2252 2832 1480 | 1202 1802 3191 3911 1122 4312 3469 37393167

Answer 1

we have given - Front له = x= Independent variable Rear. y = Dependent variable 2-C 936, 978, 2252, 2832,3911, 4312, 3469) 3167] y=C1480, 1202, 1802, 3191, 1122, 3739, n=7 observation. Is there sufficient evidence to claim

conclude that there is a linear correlation between the repair costs from Full Front Crashes and full rear crashes ? To Test Ho : p=0 H: P40 where f = Population correlation between ady Test statistic : z=rxJh-2 JI-82 where

४ correlation coefficient between 41 shay * Shay share (६+६५६) ६११ - ssay - where h 2 slan ६१२- (६१,12 (६५/- +4 ६५.2- (६५: 0 n ... ६१ - ( 936 + १+8 + 2252 + 2632 +39|| + 4312 + 3469) -- 18690

Ey; = C1480 +1202 + 1802 + 3191 + 1122 + 3739+ 3167) Eotsi Ex;? [(936)2+(978)2+(2252)2+(2832)2 + (39112+ + (4312)2 + (346912) = ( 876096 + 956484 +5071504 + 8020224 + 15295921 + 18593344 +12033901) = (60847534

६५.2 = C(1480) - + (1202)- + (1802)- +(241) + (1122)-+ (3434)-+ ( १८)] ( =(2(१०५० + १५५५80५ + 324420५ + 10\6248| + 12588१५ + 3980/21 + (602१४४१) =4233248) +- C(936 1480) + (91841202) + (2212*1802) + (2822*39\) + (११|| * \\22) + (43|2 + 243१) + (१५१ * 364)]

t - tehtalt 42333 783 - (15703)2 hass h825561 * t106981) - hest 1899 - keys + st85225 (sot si * 26981) = 47152885 :. Stay 14+ 152885 4388142 + 16122568 + 10986323] tzibeɛobt holsson tessstillt a&Zs&El ]

r = 5225875 0.5925 = 10945234 * 710 7467 t 0.5925% J5 = - 1.324870 0.805570 J i- (0:5925)2 1.6446 df = (Assume) sl, n-2 = q=0.05 il $ 2.57051 critical value Net to.os, s = df (from table)

Decision :- we reject Ho if t stat > t2121 df or -t stat < tx12,df bere t stat tal21 df here wel fail to reject Ho Conclusion There is Insufficient evidence to conclude that there is 9 linear correlation between the repair costs from full front

crashes & full rear crashes. at 420.05. 2) © using problem o find regressiah line: where = y intercept 4 } = Bo + pise + Slay RR = ý ß, a = B = slope 4 ssaa 5225875 0.4775 4 I = Car 10945234

3161.912 (hosh x st th:o) + hot hisob = f ;; = 968.4764 + (0.4+75 * ) es Jesu x = $ 4594 when LG tipald t Eotsi 968.4764 = 6981 * st th:o) = con