FTest for Variance Comparison from Independent Samples We ha

FTest for Variance Comparison from Independent Samples We have two independent samples randomly drawn from two normally distributed populations. Some information on the two samples is as follows: n1 = 23 s1 = 5.2 n2 = 19 s2 = 4.7 Let 1 and 2 be population variances. a) Test H0: 1 = 2 versus H1: 1 2 at the 0.025 significance level. b) Determine the pvalue for the test. Hint: Round off probabilities and values to 5 decimal places. Determine probabilities based on some Excel probability and value lookups

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=27.04, n1 =23
Sample 2
s2^2 =22.09, n2 =19
Fo =27.04/22.09 = 1.22408
| Fo | =1.22408
Critical Value
The Value of |F | at LOS 0.025 with d.f F(n1-1,n2-1)=F(22,18) is 2.908
We got |Fo| =1.224 & | F | =2.908
Make Decision
Hence Value of |Fo | < | F | and Here we Do not Reject Ho