Question

The following hypotheses are given. $$ \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array} $$ A random sample of eight observations from the first population resulted in a standard deviation of $10 .$ A random sample of six observations from the second population resulted in a standard deviation of 7 . At the .02 significance level, is there a difference in the variation of the two populations?

          The following hypotheses are given.
$$
\begin{array}{l}
H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\
H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2}
\end{array}
$$
A random sample of eight observations from the first population resulted in a standard deviation of $10 .$ A random sample of six observations from the second population resulted in a standard deviation of 7 . At the .02 significance level, is there a difference in the variation of the two populations?

Added by Samuel M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

07/31/2023

Step 1

Step 1: Calculate the test statistic using the formula for the F-test: $$ F = \frac{s_1^2}{s_2^2} $$ where $s_1$ and $s_2$ are the sample standard deviations. Show more…

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The following hypotheses are given. $$ \begin{array}{l} H_{0}: \sigma_{1}^{2}=\sigma_{2}^{2} \\ H_{1}: \sigma_{1}^{2} \neq \sigma_{2}^{2} \end{array} $$ A random sample of eight observations from the first population resulted in a standard deviation of $10 .$ A random sample of six observations from the second population resulted in a standard deviation of 7 . At the .02 significance level, is there a difference in the variation of the two populations?