Statistical Inference: Theory-Based Approach
The key advantage of the Chi-squared statistic is that, under certain technical conditions, the null distribution is well modelled by a mathematical model called the Chi-squared distribution. The degrees of freedom for the appropriate Chi-squared distribution equal (# rows-1) x (# columns -1), using the number of rows and columns from the original two-way table. We will consider this approximation reasonable as long as we have at least 10 observations in each cell of our two-way table (see Chapter 8 for more details).
(l) Calculate the degrees of freedom for our table. [On the left, check the box that says Show X2 output to confirm your calculation of the df, but make sure you verify how it is being calculated for this study.]
(m) Now check the box to also Overlay the theoretical chi-square distribution on your simulated null distribution. Does the theoretical model appear to reasonably describe the behavior of the null distribution? Does the p-value from the theoretical distribution appear to be similar to the p-value you estimated from the simulation?
(n) Provide a detailed interpretation of this p-value: It's the percentage of what's that do what assuming what?
(o) What conclusion about the null hypothesis would you draw from this p-value? Justify your choice.
