Variance Procedures
Calculating the Test Statistic
The Problem
Example #70: Let us test the null hypothesis that the variance of height is 196. In symbols, this is:
H0 : σ² = 196
To test this hypothesis, we collect data. The data are:
39, 51, 63, 65, 33, 19, 29, 24, 36, 37, 50, 41, 58, 78, 71, 50, 38, 82, 54, 56, 52, 50, 76, 63, 25
With this information, calculate the test statistic corresponding to the given null hypothesis.
Information given:
To summarize the above, the values of import are:
| \( s^2 \) | = | 304.5 |
|---|---|---|
| \( n \) | = | 25 |
| \( \sigma^2_0 \) | = | 196 |
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 χ² = 37.2857. Congratulations!
![[Incorrect!]](images/incorrect.png "You are not correct.")
Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.
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