Calculate the test statistic F 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. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 13 & \mathrm { n } _ { 2 } = 12 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 17.248 & \mathrm {~s} _ { 2 } ^ { 2 } = 13.75
\end{array}$$
A)1.254
B)0.797
C)1.120
D)1.573

Question

Calculate the test statistic F 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. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 13 & \mathrm { n } _ { 2 } = 12 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 17.248 & \mathrm {~s} _ { 2 } ^ { 2 } = 13.75
\end{array}$$
A)1.254
B)0.797
C)1.120
D)1.573

Quizplus · Accepted Answer

The test statistic F is calculated by dividing the larger sample variance by the smaller sample variance. Here, $F = \frac{s_1^2}{s_2^2} = \frac{17.248}{13.75} = 1.254$.

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