Consider the following competing hypotheses and accompanying

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. Use Table 2.

Solution

Set Up Hypothesis
Null Hypothesis , There Is No-Significance between them Ho: u1 >= u2
Alternate Hypothesis, There Is Significance between them - H1: u1 < u2
Test Statistic
X(Mean)=222
Standard Deviation(s.d1)=32 ; Number(n1)=12
Y(Mean)=253
Standard Deviation(s.d2)=26; Number(n2)=12
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =222-253/Sqrt((1024/12)+(676/12))
to =-2.6
| to | =2.6
Critical Value
The Value of |t | with Min (n1-1, n2-1) i.e 11 d.f is 1.796
We got |to| = 2.60452 & | t | = 1.796
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value:Left Tail - Ha : ( P < -2.6045 ) = 0.01225
Hence Value of P0.05 > 0.01225,Here we Reject Ho