Question

Suppose the local state university wants to determine whether there is a relationship between a student’s gender and a student’s major in college. The registrar was asked to randomly select 55 students and record their gender and major. The majors were grouped into categories of Natural Science (NS), Social Sciences (SS), and Humanities (H). Answer the following questions based on the results in the table below.

                 NS                  SS                  H                       Total

Men           11                    9                   3                          23

Women       9                   13                  10                        32

Total    20                   22                  13                        55

Part I: 1. Determine the expected frequency for each of the cells within the table.

2. Compute the sample chi-square statistic from the contingency table. 3. Conduct a chi-square test of independence to determine whether there is a relationship between gender and college majors. Show all of your work to support your chi-square test. 4. What conclusion can be determined from the results of the chi-square test?

Part II: Suppose we are only interested in the college majors of the women in our study. We would like to compare our sample to the national percentage of women majoring in each of the categories (NS, SS, and H) and determine whether the sample distribution fits the national distribution. Suppose the national percentage of women majoring in Natural Sciences is 22%, majoring in Social Sciences is 28%, and majoring in the Humanities is 30%.

                  NS                     SS                       H                  Total

Women 9                       13                       10                    32

1. Conduct a chi-square goodness-of-fit test to determine whether our sample data fits the national distribution. Show all of your work to support your chi-square test. 2. What conclusion can be determined from the results of the chi-square test?

Answer 1

Part I

Null hypothesis : H_o: There is no relationship between gender and college majors

Alternate Hypothesis : H_a : There is relationship between gender and college majors

Test Statistic :

O : Observed Frequency

E : Expected Frequency

Given: Observed Frequency

	NS	SS	H	Total
Men	11	9	3	23
Women	9	13	10	32
Total	20	22	13	55

1. Expected Frequency: E

	NS	SS	H	Total
Men	(23*20)/55	(23*22)/55	(23*13)/55	23
Women	(32*20)/55	(32*22)/55	(32*13)/55	32
Total	20	22	13	55

	NS	SS	H	Total
Men	8.3636	9.2	5.4364	23
Women	11.6364	12.8	7.5636	32
Total	20	22	13	55

2. Chi-square test statistic:

O	E	(O-E)	(O-E)2	(O-E)2/E
11	8.3636	2.6364	6.9504	0.8310
9	9.2	-0.2000	0.0400	0.0043
3	5.4364	-2.4364	5.9359	1.0919
9	11.6364	-2.6364	6.9504	0.5973
13	12.8	0.2000	0.0400	0.0031
10	7.5636	2.4364	5.9359	0.7848
			Total	3.3125

3. Degrees of freedom = (number of rows - 1) * ( number of columns - 1) = (2-1)*(3-1) = 1*2 = 2

Let Level of significance = 0.05 ; as p-value : 0.1909 is greater than 0.05 ; Fail to reject null hypothesis.

There is not sufficient evidence to conclude that There is relationship between gender and college majors

i.e there is no relation ship between gender and college majors