Back to our Introductory Example

We are now able to calculate the exact value of the 0.95 quantile of our test statistics.

Because the value of our test statistics is 5.85062, we will reject the null hypothesis. Approximating the null distribution of our test statistics by the chi-square distribution with 2 degrees of freedom--the 0.95 quantile of this distribution is 5.99145--we would not be able to reject the null hypothesis. This example shows that it is important to work with the exact values of quantiles and not with their approximations.