Your friend has tuned up his drag ricer and claims he can al

Your friend has tuned up his drag ricer and claims he can always average under 9 seconds in a 1/4 mile. You set up a test and find his times are the following: 8.57 9.05 8.43 9.12 8.15 a.) Can you support his claim with 95% certainty? Prove or disprove using a formalized hypothesis test. b.) At what confidence level could you support his claim?

Solution

t-test For Single Mean
Set Up Hypothesis
Null Hypothesis H0: U=9
Alternate Hypothesis H1: U<9
Test Statistic
Population Mean(U)=9
Sample X(Mean)=8.664
Standard Deviation(S.D)=0.4137
Number (n)=5
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =8.664-9/(0.4137/Sqrt(4))
to =-1.816
| to | =1.816
Critical Value
The Value of |t ?| with n-1 = 4 d.f is 2.132
We got |to| =1.816 & | t ? | =2.132
Make Decision
Hence Value of |to | < | t ? | and Here we Do not Reject Ho
P-Value :Left Tail -Ha : ( P < -1.8161 ) = 0.07176
Hence Value of P0.05 < 0.07176,Here We Do not Reject Ho

a) We conclude that we don\'t support the claim

b)
at 90% COnfidence level we support the claim