I NEED HELP ASAP! THANKS!

Question

Test the Hypothesis that the variance of two populations are the same at 90% confidence level. The two sample variance are 8 with 40 degree of freedom and 12 with 50 degree of freedom.

a.) what is the F statistic? can you reject the null hypothesis? Why?

b.) if we change to 95% confidence level, will your conclusion change? Why?

Answer 1

The hypotheses are that the two populations are normally distributed, and that the samples are randomly and independently selected.

 

Then,

 

H₀: σ₁² = σ₂²

H_A: σ₁² ≠ σ₂²

 

This is a two-tailed test, so we use α/2 = .05

 

F = 8/12 = 0.667

 

where D₁=40-1=39, and D₂=50-1=49

 

The critical F value from a table is 1.634. Since F ≤ 1.634, we do not reject the null hypothesis . There is not sufficient evidence to support the hypothesis that the two populations have different variances.

 

For part (b), look up the critical F value corresponding to alpha= .025. However, you can also point out that .025<.05, and since we did not reject at 0.05, we will not reject at 0.025.

 

I hope that helps.