Difference in the variation of the two populations

Question

Discussion:

Q1: The following hypothesis are given:
Ho= σ₁² = σ₂²
H1= σ₁² ≠ σ₂²

A random sample of eight observations from the first population resulted in a standard deviation of 10. A random sample of six observations from the second population resulted in a standard deviation of 7. At the .02 significance level, is there a difference in the variation of the two populations?

Q2: The following hypothesis are given:

Ho= σ₁² ≤σ₂²
H1= σ₁²> σ₂²

A random sample of five observations of five observations from the first population resulted in a standard deviation of 12. A random sample of seven observations from the second population showed a standard deviation of 7. AT the .01 significance level, is there more variation in the first population?