Question

How many degrees of freedom does the chi-square test statistic for a goodness of fit have when there are 10 categories?

Answer 1

Answer:

$df = n-1=10-1=9$

a. 9

Step-by-step explanation:

Previous concepts

A chi-square goodness of fit test "determines if a sample data matches a population".  

A chi-square test for independence "compares two variables in a contingency table to see if they are related. In a more general sense, it tests to see whether distributions of categorical variables differ from each another".  

We assume that we have the following system of hypothesis:

H0: The data follows the distribution proposed

H1: The data not follows the distribution proposed

The statistic to check the hypothesis is given by:  

$\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}$  

This statistic have a Chi Square distribution distribution with k-1 degrees of freedom, where n represent the number of categories on this case k=10. And if we find the degrees of freedom we got:

$df = k-1=10-1=9$

a. 9