1Two different brands of batteries are tested and the variat

1.Two different brands of batteries are tested and the variations of their voltage outputs are noted. The table gives the data. At a 5% significance level, thest the claim that the populations of the two brands have the same voltage variations.

Brand A: n=10 x bar= 9.31 s=.37

Brand B: n=8 x bar= 8.82 s=.31

Give the null and alternative hypotheses, Find the critical value of this F-test, find the test value for variances, reject null hypothesis or not, conclusion.

Solution

Testing the Difference Between Two Variances
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=0.37, n1 =10
Sample 2
s2^2 =0.31, n2 =8
Fo =0.37/0.31 = 1.19
| Fo | =1.19
Critical Value
The Value of |F | at LOS 0.05 with d.f F(n1-1,n2-1)=F(9,7) is 4.823
We got |Fo| =1.194 & | F | =4.823
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho