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.

Answer 1

Given that, population mean(u)=36000 sample mean, x = 34367 standard deviation, s =5110 number (n)=60 null, Ho: u>=36000; alternate, H1: u<36000 level of significance, alpha = 0.01 from standard normal table,left tailed t alpha/2 = 2.391 since our test is left-tailed reject Ho, if to < -2.391 we use test statistic (t) = x-u/(s.d/sqrt(n)) to = 34367-36000/(5110/sqrt(60)) to =-2.4754 to | = 2.4754 critical value; the value of It alpha with n-1 = 59 d.f is 2.391 we got to = 2.4754 & t alpha = 2.391 make decision; hence value of to | > | t alpha and here we reject Ho p-value :left tail - Ha: (p < -2.4754 ) = 0.0081 hence value of po.01 > 0.0081, here we reject Ho null, Ho: u>=36000; alternate, H1: u<36000 test statistic: -2.4754 critical value: -2.391 decision: reject Ho p-value: 0.0081,no evidence to support the manfacture's claim