Question

A manufacturer of discount tires announced that its tires can be driven for at least 36,000 miles before wearing out. You suspect that the manufacturer's claim is false and decide to test the tires. In order to determine the average number of miles that discount tires can be driven for, a random sample of 60 tires is selected from the manufacturer's warehouse and the tires are tested independently until they wear out. The sample mean number of miles driven before the tires wore out was 34,367 miles and the sample standard deviation was 5,110 miles. a. Use a hypothesis test with the 7-step method and the critical value alternative to verify if there is enough significant evidence (a = 0.01) to conclude that the manufacturer's claim is false Interpret your findings b. Calculate the p-value for the test statistic. c. Use R to justify the results of the hypothesis test (and include the R output)

Answer 1

Solution Griven lo= 36000 miles n=60 a sample mean = x= 34 367 miles 220.0 Sample standar Deration - Se suo miles claim: A manufacture of discount tires announced that its tires can be chinen for at least 36000 miles. Here, &- is unknown so we use t- test To step-0 Hypothesis Step ② To test Holly, Mo=36000 Vs H: 4 < to - (one failed test) ! step. To find test statistic I under to the test statistic is, to = X-llo - 34367 - 36000 - - 2.48 . S/h 5110/460 (calculated a value step- Table value tn 12 - trool, oool o - tsgroot This value not seen in t-table so we find this value using ms- Excel command "TENV (0.02, 59) =-2.3912 step-6 L Decision Rule Here to = - 2.48 hence we reject Ho at t. 1.0.5. ttab= -2.39/2

step 6 construct the rejection region. probability Proborary density cune 72 th-1,2= 259,9.00 = -2.3912 step ② Conclusion We conclude that there is enough significant endence the manufacturer's claim is tale. R A & manufacture of discount tires announced that its tires can not be driven for at least 36000 miles. 6 we calculate p-value as follow; p-value - pl tn-l to] = p Its g L-2.48) (due to symmetry - Pl tog > 2:48] By using ms- Excel Command By using "TOIST (2.48, 59, 1) -0.0080 p-value = 0.0080 a 1.o.s. - 2500l hence we. geject to at lt. d.o.s. Using R to justify results of hypothesis test (Included the Routput) ©