Use the sliders to change the degrees of freedom and the chi-squared statistic. See how this affects the graph of the chi-squared distribution and the associated p-value. Answer the questions below.

What does the chi-squared statistic represent about your data?

What does the p-value represent about your data?

What happens to the p-value as the chi-squared statistic increases? As it decreases? Why is this?

If you wanted to make sure you only reject your null hypothesis when the observed data is very different from what you expect, would you choose a small or large p-value?

Does a table with many rows and columns have large or small degrees of freedom? How do you know?

What happens to the shape of the graph as the degrees of freedom increases?

Estimate the chi-squared statistic that corresponds to a p-value of 0.1 for the following degrees of freedom: 2, 4, 6, 8.

Based on your estimates above, as the degrees of freedom increase, what happens to the chi-squared values corresponding to a set p-value? Why is this?