Question

Freshman, sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracurricular student activities fee. There are three possible responses to the survey question - agree with the increase, do not agree with the increase, or no opinion. A chi-square test will be conducted to determine whether the response to this question is independent of the class in which the student is a member. How many degrees of freedom should the chi-square test have

Answer 1

The degrees of freedom is 6 for the chi square independence test.

Explanation:

This is test hypothesis of independence. The test statistic under H0 is

χ²= ∑ (O - E)²/ E

where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( r-1) (c-1) degrees of freedom, where r= rows and c= columns.

Here there are 4 rows and 3 columns

Hence the degrees of freedom will be

( 4-1) ( 3-1)= 3*2= 6