Question

Stephanie is curious in knowing whether there is a relationship between gender and the area of interest. She randomly sampled some students and collects the following info. Her objective is find out if the gender influences the choice of the field to study.

	Science	Arts	Business	Total
Male	27	28	45	100
Female	20	41	54	115
Total	47	69	99	215

1. How many degrees of freedom should she use for the Chi-Square test?

2. What is the Chi-Squared statistic for this test?

3. What is P-value for this test? Use Excel's CHISQ.DIST function.

4. Based on the Chi-Squared test for Independence, can you say that the gender and the choice of study field are independent?

Answer 1

Solution:

Given: We have to test if there is a relationship between gender and the area of interest. Objective is find out if the gender influences the choice of the field to study.

Thus hypothesis of the study are:

H0: the gender and the choice of study field are independent

Vs

H1: the gender and the choice of study field are not independent

	Science	Arts	Business	Total
Male	27	28	45	100
Female	20	41	54	115
Total	47	69	99	215

Part 1. How many degrees of freedom should she use for the Chi-Square test?

df = ( R - 1) X ( C - 1)

R = Number of rows = 2

C = Number of Columns = 3

Thus

df = ( R - 1) X ( C - 1)

df = ( 2 - 1) X ( 3 - 1)

df = ( 1) X ( 2)

df = 2

Thus degrees of freedom = 2

Part 2. What is the Chi-Squared statistic for this test?

Formula:

O_ij = Observed frequencies for i^th row and j^th column.

E_ij = Expected frequencies for i^th row and j^th column.

Thus we need to make following table in column format:

Oij	Eij	Oij2/Eij
27	21.8605	33.348
28	32.0930	24.429
45	46.0465	43.977
20	25.1395	15.911
41	36.9070	45.547
54	52.9535	55.067
N = 215

Part 3. What is P-value for this test? Use Excel's CHISQ.DIST function.

For Chi-square goodness of fit test, it is always right tailed test and hence we use following excel command:

=CHISQ.DIST.RT( x ,   df )

=CHISQ.DIST.RT( 3.279 , 2)

=0.1941

Thus P-value = 0.1941

Part 4. Based on the Chi-Squared test for Independence, can you say that the gender and the choice of study field are independent?

Since P-value = 0.1941 > 0.05 significance level, we fail to reject null hypothesis H0.

Thus we conclude that: the gender and the choice of study field are independent