The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are

The expected frequencies for all categories are at least 5.

Step-by-step explanation:

The chi-square goodness of fit test is useful when we have one categorical variable from a population. The test is used to determine whether the data collected are consistent with a hypothesized distribution.

The conditions required to use the chi-square goodness of fit test are:

The degrees of freedom of this test is:

d = k - 1

Here,

k = number of categories.

Thus, the expected frequencies for all categories are at least 5.

answer: (1,3) and (-2,0) i think.