Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma \underset { 1 } { 2 } \neq \sigma _{ 2 }^{ 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.02$$ $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 0.578 & \mathrm {~s} _ { 2 } ^ { 2 } = 0.260
\end{array}$$
A)3.59
B)2.45
C)2.92
D)4.56

Question

Find the critical value $$\mathrm { F } _ { 0 }$$ to test the claim that $$\sigma \underset { 1 } { 2 } \neq \sigma _{ 2 }^{ 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.02$$ $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 18 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 0.578 & \mathrm {~s} _ { 2 } ^ { 2 } = 0.260
\end{array}$$
A)3.59
B)2.45
C)2.92
D)4.56

Quizplus · Accepted Answer

The critical value for an F-test is determined by the degrees of freedom and the significance level. Here, the degrees of freedom are $ n_1 - 1 = 10 $ and $ n_2 - 1 = 17 $. Using an F-distribution table or calculator with $\alpha = 0.02$ for a two-tailed test, the critical value is approximately 3.59.

Find the Critical Value F0\mathrm { F } _ { 0 }F0​

Find the Critical Value $\mathrm { F } _ { 0 }$