Question

The National Highway Traffic Safety Administration (NHTSA) claims that, in a car accident, Tesla passengers are less likely to be injured than their non-Tesla counterparts. They select a random sample of 200 Tesla passengers and 400 non-Tesla passengers who were in a car accident. From their data, they found that 5.5% of the Tesla passengers and 9% of the non-Tesla passengers were injured. Test the NHTSA’s claim at a 10% significance level.

a) Define Population 1 and Population 2.

b) Define the parameter and random variable of interest.

c) State the null and alternative hypotheses, and identify the claim.

d) Determine the distribution of the test statistic. (Check the relevant criteria.)

e) Calculate the test statistic.

f) Find the p-value.

g) State your decision.

h) State your conclusion.

Answer 1

(a population 1 - Tesla passengers population a - Non Tesla Passengers (6) Let Py = population proportion Tesla passenger P = Population proportion Non Tesla passengas (c) Noll hypothesis (Ho): P, SP (or) P = P, Abbonative hypother's (Ha): P, che Z-test for too proportion test sladistic is used Talstatistics @ @ -B, where wober 1, 200 2 = = : 400 PO G +0.055 P, :0.09 i napit nal. - 200(0.055) 460(6.09 200 400 = 0.0783 © 21-P1-0.0783 =0.921 0.055 -0.09 Z : 0.0483(0.9217) (1 200" Yoo) -0.035 0.0233 2 = -1.50 (f) with Z=-1.50 Clept failed) we get [P-value = 0.0668) (9) Decision: P-value > Lois 0.0668 > 0.10 So fail to deject Ho (h) conclusion: At 2 20.10 los there is no evidence to claim thad Tesla passengers ase lass likely to be injosed than their non desta coundesports.