Do these data provide sg evidence at 46 level for M1 Solutio

Do these data provide s.g. evidence at 4.6% level for M_1

Solution

Set Up Hypothesis
Null , u1 below t Ho: u1 - u2 = 20
Alternate , - H1: u1 - u2 != 20
Test Statistic
X(Mean)=104.23
Standard Deviation(s.d1)=45.45 ; Number(n1)=41
Y(Mean)=62.24
Standard Deviation(s.d2)=16.34; Number(n2)=49
we use Test Statistic (t) = (X-Y)- ( U1 - U2)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =((104.23-62.24)-20)/Sqrt((2065.7025/41)+(266.9956/49))
to =21.99/Sqrt((2065.7025/41)+(266.9956/49))
to =2.942
| to | =2.942
Critical Value
The Value of |t a| with Min (n1-1, n2-1) i.e 40 d.f is 1.796
We got |to| = 2.942 & | t a | = 1.796
Make Decision
Hence Value of | to | > | t a| and Here we Reject Ho
P-Value:Right Tail -Ha : ( P > 2.942 ) = 0.0027
Hence Value of P0.01 > 0,Here we Reject Ho