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. $$\begin{array} { l l }
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 4800 & \mathrm {~s} _ { 2 } ^ { 2 } = 1875
\end{array}$$
A)2.560
B)1.600
C)0.391
D)6.554

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. $$\begin{array} { l l } 
\mathrm { n } _ { 1 } = 16 & \mathrm { n } _ { 2 } = 13 \\
\mathrm {~s} _ { 1 } ^ { 2 } = 4800 & \mathrm {~s} _ { 2 } ^ { 2 } = 1875
\end{array}$$
A)2.560
B)1.600
C)0.391
D)6.554

Quizplus · Accepted Answer

The test statistic F is calculated as:$$F = \frac{s_1^2}{s_2^2}$$Substituting the given values, we get:$$F = \frac{4800}{1875} = 2.560$$Therefore, the correct answer is A.

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