Question

You are interested in investigating whether gender and major are associated at your college. The table below shows the results of a survey.

Frequencies of Majors and Gender

	Math/Science	Arts/Humanities	Business/Econ.	Other
Men	83	89	100	56
Women	106	126	100	31

What can be concluded at the αα = 0.01 significance level?

1. What is the correct statistical test to use?
   • Independence
   • Homogeneity
   • Paired t-test
   • Goodness-of-Fit
2. What are the null and alternative hypotheses?
   H0:H0:
   • College major and gender are dependent.
   • The distribution of college major is the same for each gender.
   • College major and gender are independent.
   • The distribution of college major is not the same for each gender.
   
   
   
   H1:H1:
   • The distribution of college major is not the same for each gender.
   • College major and gender are independent.
   • College major and gender are dependent.
   • The distribution of college major is the same for each gender.
3. The test-statistic for this data =  (Please show your answer to three decimal places.)
   
4. The p-value for this sample = (Please show your answer to four decimal places.)
   
5. The p-value is Select an answer less than (or equal to) greater than  αα
   
6. Based on this, we should
   • accept the null
   • reject the null
   • fail to reject the null
7. Thus, the final conclusion is...
   • There is sufficient evidence to conclude that the distribution of college major is not the same for each gender.
   • There is sufficient evidence to conclude that college major and gender are independent.
   • There is sufficient evidence to conclude that college major and gender are dependent.
   • There is insufficient evidence to conclude that the distribution of college major is not the same for each gender.
   • There is insufficient evidence to conclude that college major and gender are dependent.

Answer 1

correct statistical test to use? Independence

2) Ho:College major and gender are independent.

H1: College major and gender are dependent.

3)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Math/Science	Arts/Himanities	Business/Econ	Other	Total
	Men	89.71	102.05	94.93	41.30	328
	Women	99.29	112.95	105.07	45.70	363
	total	189	215	200	87	691
chi square    χ2	=(Oi-Ei)2/Ei	Math/Science	Arts/Himanities	Business/Econ	Other	Total
	Men	0.5024	1.6700	0.2702	5.2350	7.6776
	Women	0.4539	1.5090	0.2442	4.7302	6.9374
	total	0.9563	3.1790	0.5144	9.9652	14.6150
test statistic X2 =		14.615

The p-value for this sample =0.0022

The p-value is less than alpha

reject the null

There is sufficient evidence to conclude that college major and gender are dependent.