Question

3. It is believed that incan brimper ropair costs for low speed crashes is less for small cars than it is for midsize cars. In order to test this claim, the following data was collected on a sample of sınall cars and a sample of midsize enrs. Small Car Midsize Car My = 12 12 = 16 *, - $ 173 * = $741 8; - $1909, - $205 Assume that the repair costs are normally distributor with equal population vari- ances. (a) (2 points) Set np the null and alternative hypotheses to test the claim. Ho H.: (b) (5 points) Phed the value of the appropriate standardized test statistic and sny whether it is a t or . OD Sol lol comba (c) (5 points) Find the rejection region al 1% significance level. S- (d) (3 points) State your conclusion in the context of the problem.

Answer 1

Kindly see the attached solution for hypothesis testing

Given Ismoll Car 12 x 3543 Si=1120 Let be the pepen transmell de midsize cor the claim to eat het men bumpet pait cost et les specel ceashes is less je Small leares than it is for midsize con w The hypothesis to be tested is Ho: el, M. uls Holz <h₂ b) Test statistic Heee sample size is 56 d population standard deviation is unknown hence that is wed The Trst statistics X-3) - 64,-.) where sp - Pooled standaed decision Sp=cn. 1352 + (0₂1) 5² (12-1) (190)² + (16-1) (2057 12 +1E-2 1136100)+(15*42015)

Page 2 59100603 10211 198.79 SpJ5931527198792 se 198.79 The t-test state will be 198-19 x 0.38188 to -3.53 The test statistic value is t= -3.53 o Rejechon region at signifitance The olle native hypothesis is one failed The ejection cegien hoe left teiled alternative hypothesis is Heze the degree of freedom Reection tip e 1.11.-2.26 0.01 The t critical value at - 26 degrees of freedom fez 0.01 test dailed peobability is - 2.473 Feveres terit & -2.478 -terit

- Page 3 The eglection region to the tests Rection frien 2.45 di Conclusion Here at deject null hypothesis is calcul t-test statistic lies in tejection tegien Inle reject nu hypothesis is Cottorit -2.48 Colt -3.55 t-test statistie -3.53 - 2:48 Henet toe deject the nun hypothesis Conclude that mean bumpe zepuis cast for low speed crashes is less for small cats than foc midsize cars