There are four major political parties in the country Treon. A public research group is interested in finding out whether there is any relationship between the party that is supported by a citizen of Treon and that citizen's socio-economic status. For the purposes of a study, socio-economic status is broken up into four different categories: poverty, working class, middle class, and upper class.

Question

There are four major political parties in the country Treon. A public research group is interested in finding out whether there is any relationship between the party that is supported by a citizen of Treon and that citizen's socio-economic status. For the purposes of a study, socio-economic status is broken up into four different categories: poverty, working class, middle class, and upper class.

A survey is conducted where many people are asked which major party they vote for and their socio-economic status. The data from this survey is used in the ÷2 hypothesis test with 95% confidence and the following hypotheses:

H0: There is no relationship between party affiliation and socio-economic status.

H1: There is a relationship between party affiliation and socio-economic status.

The test statistic for this test is calculated to be 13.845.

a) Calculate the number of degrees of freedom (df) in the ÷2 distribution that is followed by this test statistic. Give your answer as a whole number.

df =

b) The null hypothesis (is or is not) rejected

Answer 1

I don't know what you mean by "the ÷2 distribution."

Answer 2

sorry it means an chi squared test x^2

Answer 3

a) To calculate the number of degrees of freedom (df) in the χ² distribution, we need to know the number of categories or levels for each variable in the study.

In this case, there are 4 major political parties in Treon and 4 socio-economic status categories. The degrees of freedom for a χ² test is calculated as (Number of rows - 1) * (Number of columns - 1).

Number of rows = Number of political parties = 4
Number of columns = Number of socio-economic status categories = 4

df = (4 - 1) * (4 - 1) = 3 * 3 = 9

Therefore, the number of degrees of freedom (df) in the χ² distribution for this test is 9.

b) To determine whether the null hypothesis is rejected or not, we compare the calculated test statistic (13.845) with the critical value from the χ² distribution at a 95% confidence level. If the calculated test statistic is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

However, since the critical value is not provided in the question, we cannot determine whether the null hypothesis is rejected or not with the given information.