Final answer:
A goodness-of-fit test is used to assess whether a data set fits a specific distribution. The null hypothesis states that the data come from the assumed distribution, while the alternative hypothesis states that the data do not follow the assumed distribution.
Step-by-step explanation:
Goodness-of-Fit Test
A goodness-of-fit test is used to assess whether a data set fits a specific distribution. The null hypothesis states that the data come from the assumed distribution, while the alternative hypothesis states that the data do not follow the assumed distribution. In this case, if the expected numbers per column are 25% each, the null hypothesis would be that the observed frequencies match the expected frequencies, and the alternative hypothesis would be that they do not.
Degrees of Freedom
The degrees of freedom for a goodness-of-fit test are equal to the number of categories minus 1. In this case, since there are 4 categories (columns), the degrees of freedom would be 4 - 1 = 3.