Given two samples of sizes n110 and n2 9 drawn from two popu

Given two samples of sizes n1=10 and n2= 9  drawn from two populations N(1 ,1^{2 )}   and N(2, 2² ) respectively. These samples gave the following sample variances S1²=11.5 and S2²= 13.1  respectively. By using the p-value approach, Test the hypothesis H₀:1²   2² against    H₁: 1² > 2²   (for =0.01)

Solution

Null Hypothesis, There Is No Significance between them Ho: ^2 <= ^2
Alternate Hypothesis, There Is Significance between them H1: ^2 > ^2
Test Statistic
Sample 1
s1^2=11.5, n1 =10
Sample 2
s2^2 =13.1, n2 =9
Fo =11.5/13.1 = 0.88
| Fo | =0.88
Critical Value
The Value of |F | at LOS 0.01 with d.f F(n1-1,n2-1)=F(9,8) is 5.911
We got |Fo| =0.878 & | F | =5.911
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho