Calculating the Test Statistic

In the box below, please enter the test statistic for the null hypothesis and the data given above. Once you have done so, click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

Your guess:

You got the correct answer of F = 1.584. Congratulations!

Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.

Show Formula

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Here is the formula you can use to calculate the confidence bounds.

Since we hypothesize that the two population variances are equal, the second ratio is 1. This leads to the following formula:

In this formula, there are a few symbols to know:

Show Solution

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Thus, the observed test statistic is 1.584. You would then compare this to the critical value from the F distribution with \(\nu_1 = n_1 - 1\) = 17 and \(\nu_2 = n_2 - 1\) = 17.

Show the R Code

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Copy and paste the following code into your R script window, then run it from there.

In the R output, the test statistic is the number that follows “F =” near the top. Note that R will give you test statistics that are more accurate and more precise than doing the calculations by hand. As such, these computer-calculated limits will differ slightly from those you calculate by hand.

Show the Excel Code

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Copy and paste the following code into your Excel window, making sure the value sample1 ends up in A1 after pasting.

The test statistic is located in cell D6. Again, when you paste this code into Excel, make sure that you start the pasting in cell A1. To help with that, you may want to also copy this notice. It seems to help.