Variance Procedures
Calculating the Test Statistic
The Problem
Example #181: Let us test whether the variance of population 1 differs from that of population 2. In symbols, this is:
H0 : σ²1 /σ²2 = 1
HA : σ²1 /σ²2 ≠ 1
To test this hypothesis, we collect data. The data from population 1 are:
31, 33, 43, 4, 35, 13, 12, 35, 13, 25, 26, 15, 19, 34, 26, 33
The data from population 2 are:
41, 45, 36, 16, 26, 38, 31, 35, 36, 17, 44, 20, 35, 27, 34, 3, 20, 25
With this information, calculate the test statistic corresponding to the null hypothesis.
Information given:
To summarize the above, the values of import are:
| \( \sigma^2_0 \) | = | 1 |
|---|---|---|
| \( s_1^2 \) | = | 120.295833 |
| \( n_1 \) | = | 16 |
| \( s_2^2 \) | = | 122.486928 |
| \( n_2 \) | = | 18 |
It may be helpful if you calculate these values yourself. Once you have, you can check your answers by hovering your mouse over the grey spaces to see if you calculated them correctly.
Your Answer
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.
![[Correct!]](images/correct.png "You are correct. Well done!")
You got the correct answer of F = 0.9821. Congratulations!
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