Find the critical value $$F _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } \sigma _{ 2 }^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.01 .$$ $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 1600 & \mathrm {~s} _ { 2 } ^ { 2 } = 625
\end{array}$$
A)4.01
B)3.18
C)2.62
D)3.67

Question

Find the critical value $$F _ { 0 }$$ to test the claim that $$\sigma _ { 1 } ^ { 2 } > \sigma _{ 2 }^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. Use $$\alpha = 0.01 .$$ $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 1600 & \mathrm {~s} _ { 2 } ^ { 2 } = 625
\end{array}$$
A)4.01
B)3.18
C)2.62
D)3.67

Quizplus · Accepted Answer

To find the critical value $F_{0}$ for the given hypothesis test $\sigma_{1}^{2} > \sigma_{2}^{2}$ at $\alpha = 0.01$, we use the F-distribution. The degrees of freedom for the numerator ($df_1$) is $n_1 - 1 = 16 - 1 = 15$ and for the denominator ($df_2$) is $n_2 - 1 = 13 - 1 = 12$. Looking up the critical value in the F-distribution table for $\alpha = 0.01$, $df_1 = 15$, and $df_2 = 12$, we find $F_{0} = 4.01$.

Find the Critical Value F0F _ { 0 }F0​ To Test the Claim That

Find the Critical Value $F _ { 0 }$ To Test the Claim That