If S12 and S22 are the variances of independent random sampl

If S1^2 and S2^2 are the variances of independent random samples of sizes n1 = 10 and n2 = 15 from normal populations with equal variances, find P(S1^2/S2^2

Solution

THe degree of freedom df1=n1-1=10-1=9

The degree of freedom df2=n2-1=15-1=14

The probability is

P(S1^2/S2^2 <4.03) = P(F with df1=9 and df2=14 <4.03)

=0.99 (from F table)