Question

Gender and College Major

Does gender play a role in what students decide to study in college? Although the gender gap has closed dramatically in recent years it would be interesting to see how current college age students reflect differences, or not, in their choice of college major. It is sometimes thought that the more technical areas of study are the domain of the male students. Let’s just see if there is any difference.

Below is a table of values showing the enrollment by gender in four of the popular major areas of study offered at a prestigious university.

		ACADEMIC MAJOR
		Arts	Sciences	Engineering	Education
GENDER	Female	35	15	5	25
	Male	10	40	50	20

It is difficult to analyze the data in raw form as displayed in the table. We must analyze further before attempting to answer the ultimate question. Is there any difference between what males and females decide to pursue as their college major?   There are a variety of ways to analyze these numbers: numerically, graphically, and through use of a formula. You will explore all three as you complete this task.

Answer the following questions using what you know about categorical data calculations and percents. Give complete answers with justifications. It is not acceptable to simply state a number.

I: Numerical Comparisons:
1 point
How would you describe the SHAPE of the table? Think Matrix!


1 point
How would you edit the table to be more useful? What is missing in order to convert raw counts to percents? Explain.

1 point
Among male students, what percent are majoring in engineering subjects?

1 point
Among education majors, what percent are males?

1 point
What percent of students are majoring in science?

2 points
What are the marginal distributions by gender?

5 points
Do you think that gender and choice of major are related or NOT?
Give statistical evidence to support your claim.

II. Graphical Comparisons
4 points
One way to display categorical data is through the use of pie charts. This problem requires TWO pie charts, one for each gender. Create and comment on those gender pie charts. What features are evident in the graphs?



III. Formula Method:
4 points
Given the formula for EXPECTED counts in any cell to be

Expected frequency =   (row total)(column total)/
                                                    TOTAL of all

Pick any cell and use your findings to either confirm or reject your previous statement. Explain.

Answer 1

Using the table given below

Table(1)

		Academic Major
		Arts	Sciences	Engineering	Education	Total
Gender	Female	35	15	5	25	80
	Male	10	40	50	20	120
	Total	45	55	55	45	200

I: Numerical Comparisons:
1 point
How would you describe the SHAPE of the table? Think Matrix!
shape is 2*4

1 point
How would you edit the table to be more useful? What is missing in order to convert raw counts to percents? Explain.
we can divide frequency of each block by total sample size to get joint pmf /percents

1 point
Among male students, what percent are majoring in engineering subjects?

P(Enginnering| Male) = P(Engineering and Male)/P(Male) = 50/120 = 5/12

1 point
Among education majors, what percent are males?
P(Males| Education) = 20/45 = 4/9

1 point
What percent of students are majoring in science?
= P(Science ) = 55/200 = 11/40