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?