Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 15 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 12.615 & \mathrm {~s} _ { 2 } ^ { 2 } = 11.76
\end{array}$$
A)1.073
B)0.932
C)1.036
D)1.151

Question

Calculate the test statistic F to test the claim that $$\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }$$ Two samples are randomly selected from populations that are normal. The sample statistics are given below. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 15 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 12.615 & \mathrm {~s} _ { 2 } ^ { 2 } = 11.76
\end{array}$$
A)1.073
B)0.932
C)1.036
D)1.151

Quizplus · Accepted Answer

The F statistic is calculated by dividing the variance of the first group by the variance of the second group: $F = \frac{s_1^2}{s_2^2} = \frac{12.615}{11.76} = 1.073$.

Calculate the Test Statistic F to Test the Claim That σ12≤σ22\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }σ12​≤σ22​

Calculate the Test Statistic F to Test the Claim That $\sigma _ { 1 } ^ { 2 } \leq \sigma _ { 2 } ^ { 2 }$