a company manufactures brackets for an auto maker regularly

a company manufactures brackets for an auto maker regularly selects brackets from the production line and perform a torque test. the goal is for the mean torque to equal 125. if a sample of 10 observations given at below, what would be the conclusion (mean equals 125 or not) at alpha=0.10? Assume data are normal. Make decision based on p-value. 128,149,136,114,126,142,124,136,122,118.

Solution

Set Up Hypothesis
Null, H0: U=125
Alternate, H1: U!=125
Test Statistic
Population Mean(U)=125
Sample X(Mean)=129.5
Standard Deviation(S.D)=11.0277
Number (n)=10
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =129.5-125/(11.0277/Sqrt(9))
to =1.29
| to | =1.29
Critical Value
The Value of |t | with n-1 = 9 d.f is 1.833
We got |to| =1.29 & | t | =1.833
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value :Two Tailed ( double the one tail ) -Ha : ( P != 1.2904 ) = 0.2291
Hence Value of P0.1 < 0.2291,Here We Do not Reject Ho