A national tire manufacturer Machelin has a popular all seas

A national tire manufacturer Machelin has a popular all season treaded tire meant for use on light trucks and SUVs and according to the company, the average tread wear for this tire should be 63 thousand miles. 40 tires (10 Cars) were randomly selected and driven until they were in need of replacement. The results of the test were a mean tread wear of 61.2 thousand miles with a standard deviation of 1.8 thousand miles. Historically the true tread wear of ALL tires for Machelin vary by 1.57 thousand miles. Perform a complete test of hypotheses to determine if there is evidence to claim the tires produced by Machelin wear out too fast. Include a P-value with the test.

Solution

Set Up Hypothesis
Null, H0: U=63
Alternate, H1: U<63
Test Statistic
Population Mean(U)=63
Sample X(Mean)=61.2
Standard Deviation(S.D)=1.8
Number (n)=40
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =61.2-63/(1.8/Sqrt(40))
to =-6.325
| to | =6.325
Critical Value
The Value of |t | with n-1 = 39 d.f is 1.304
We got |to| =6.325 & | t | =1.304
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -6.3246 ) = 0
Hence Value of P0.1 > 0,Here we Reject Ho

there is evidence to claim the tires produced by Machelm wear
out too fast