Answer:
Desision is to not reject the null hypothesis, this means that the variance of the second population is equal or greater than the variance of the first population.
Step-by-step explanation:
Hello!
You have the hypothesis set:
H₀: δ₁² ≤ δ₂²
H₁: δ₁² > δ₂²
α: 0.01
To study the population variance of two populations you have to work with the F-distribution. The statistic is:
F= (S₁²/S₂²)*(σ₁²/σ₂²) ~ F[tex]_{(n1-1);(n2-1)}[/tex]
This is a one tailed test, the critical value is
[tex]F_{(n1-1); (n2-1); 1-\alpha } = F_{4; 6; 0.99} = 9.15[/tex]
If the statistic value F[tex]_{H0}[/tex] ≥ 9.15, the decision is to reject the null hypothesis.
If the value F[tex]_{H0}[/tex] < 9.15, the decision is to not reject the null hypothesis.
F[tex]_{H0}[/tex]= (S₁²/S₂²)*(σ₁²/σ₂²) = (12/7) * 1
F[tex]_{H0}[/tex]= 1.714
Desision is to not reject the null hypothesis, this means that the variance of the second population is equal or greater than the variance of the first population.
I hope you have a SUPER day!
