Chi-Squared Goodness of Fit Test is used to test how well the data in the observed sample reflects the data in the expected sample. The observed sample and the expected sample are given as histograms with the same set of bins. That is, each entry of observed and expected is a count of observations with particular characteristics (typically, the observations within a particular range). These characteristics are the same for corresponding entries of observed and expected.

Requirements for using Chi-Squared Goodness of Fit Test:

The goal is to test if the observed sample follows the same the distribution as of the expected sample.

The observed sample and the expected sample are given as histograms with the same set of bins.

The formula is:

where $\mathrm{observed}$ and $\mathrm{expected}$ are the data in the observed sample and the expected sample respectively, $N$ is the sample size of the observed and the expected samples, and $X^2$ follows a Chi-Squared distribution with $N-1$ degrees of freedom.

Determine the null hypothesis:

Null Hypothesis: The three dice are fair. (Observed sample dose not differ from expected sample.)

Substitute the information into the formula:

$x=\frac{{\left(580-570\right)}^2}{570}+\frac{{\left(354-360\right)}^2}{360}+\frac{{\left(63-64\right)}^2}{64}+\frac{{\left(3-6\right)}^2}{6}=1.791063596$

Compute the p-value:

$p-\mathrm{value}=\mathrm{Probability}\left(Xˆ2>1.791063596\right)=0.616881663760937$,      $Xˆ2˜\mathrm{ChiSquare}\left(3\right)$

Draw the conclusion:

This statistical test does not provide enough evidence to conclude that the null hypothesis is false, so we fail to reject the null hypothesis.