Assume that the populations are normally distributed. Test the hypothesis σ1≠σ2 at the α=0.05 level of significance. (a=0.05) (Sample1: N = 9 S = 3.7) (Sample2: N = 9 S = 3.1)

Question

Please show the math used to solve the problem. Sorry some people just list answer with none of the math. thanks in advance

Assume that the populations are normally distributed. Test the hypothesis σ1≠σ2 at the α=0.05 level of significance. a=0.05 

Sample1: N = 9,  S = 3.7

Sample2: N = 9,  S = 3.1

Answer 1

I think the test statistic F is the ratio of the variances: F=σ₁²/σ₂²= (3.7/3.1)²=1.4246. (Standard deviation is the square root of variance)

H₀: F=1, H₁: F≠1 at the specified confidence level of 95% (α=0.05).

The sample sizes are the same so the DOF (degrees of freedom)=9-1=8.

Since s₁>s₂ we need the right-tailed F-distribution FCDF_0.05 to find the critical value at 8 DOF for both samples. I get 3.44 from tables for the right tail of the distribution. 1.4246 is less than the critical value so we don't have sufficient evidence to conclude that the different standard deviations are significantly different, because we cannot reject H₀.