A researcher is interested in running a test to determine if

A researcher is interested in running a test to determine if there is a significant difference in the power output of an engine when run on E85 as opposed to running an engine on traditional fuel. To test this, our researcher randomly selected 27 engines that were designed to run on E85 and found the power output. Then 32 engines designed to run on traditional fuels were selected and the power was found, (all engines were of V6 class) Minitab was used to find the following possible test outputs: Please perform a complete test of hypotheses to determine if there is a significant difference in the output of the engines. In your process indicate the output that will help you get your test statistic and P-value for your test. You may assume that both samples come from normally distributed populations.

Solution

Set Up Hypothesis
Null, There Is No-Significance between them Ho: u1 = u2
Alternate,There Is Significance between them - H1: u1 != u2
Test Statistic
X(Mean)=140.2
Standard Deviation(s.d1)=21.5 ; Number(n1)=27
Y(Mean)=148.9
Standard Deviation(s.d2)=19.5; Number(n2)=27
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =140.2-148.9/Sqrt((462.25/27)+(380.25/27))
to =-1.56
| to | =1.56
Critical Value
The Value of |t | with (n1+n2-2) i.e 52 d.f is 1.675
We got |to| = 1.55746 & | t | = 1.675
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho
P-Value: Two Tailed ( double the one tail ) - Ha : ( P != -1.5575 ) = 0.131
Hence Value of P0.05 < 0.131,Here We Do not Reject Ho

Reslut:
There is no significance diffrence b/w them