The degrees of freedom for goodness-of-fit chi-square tests are calculated with the formula: df=bins(or categories)−1−number of parameters of the distribution and the degrees of freedom for the chi-square are calculated using the following formula: df = (r-1)(c-1) .
In the given question we have to calculate degrees of freedom for goodness-of-fit chi-square tests versus chi-square tests for independence and homogeneity.
When a categorical variable has more than two levels, a chi-square goodness-of-fit test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
The degrees of freedom in this case are calculated with the formula:
df=bins(or categories)−1−number of parameters of the distribution.
The degrees of freedom for the chi-square are calculated using the following formula:
df = (r-1)(c-1)
where r is the number of rows and c is the number of columns.
The null hypothesis can be rejected if the observed chi-square test statistic is higher than the crucial value.
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