Question

A survey of 13,464 students in a country who enrolled in private career colleges was conducted to understand student participation in the private postsecondary educational system. In one part of the survey, students were asked about their field of study and about when they entered college. Here are the results Time of Entry Field of Number of Study Students Right After High School Later Trades Design Health Media/IT 3178 Service Other 34% 47% 40% 3190 36% 52% 982 574 5055 66% 53% 6096 6996 64 % 48% 1380 2295 In this table, the second column gives the number of students in each field of study. The next two columns give the marginal distribution of time of entry for each field of study (a) Use the data provided to make the 6 x 2 table of counts for this problem Time of Entry Field of Study Trades Design Health Media/IT Service Other Right After High School Later

Answer 1

(a)

	Right After	Later
Trades	333.88	648.12
Design	269.78	304.22
Health	2022	3033
Media	985.18	2192.82
Service	496.8	883.2
Other	1193.4	1101.6
	5301.04	8162.96

(b) The most popular field of study is health with (5055/13464)*100% = 37.5% of these students . The least popular field of study is Design with 4.3% of these students . Overall (5301.04/13464)*100%= 39.4% of students enrolled right after high school .

(c) H0: There is not an association between field of study and when students enter colleges.

Ha: There is an association between field of study and when students enter colleges.

Test statistic,

(Oi - Ei)2

where Oi : observed frequency

Ei : expected frequency

Calculation :

Oi	Ei	(Oi-Ei)^2/Ei
333.88	386.6326	7.197625
269.78	225.995	8.48303824
2022	1990.252	0.50642592
985.18	1251.241	56.5744928
496.8	543.333	3.98525034
1193.4	903.5864	92.9539745
648.12	595.3674	4.67414982
304.22	348.005	5.50889935
3033	3064.748	0.32887385
2192.82	1926.759	36.7395711
883.2	836.667	2.5880283
1101.6	1391.414	60.3644679
		279.904797

Where Ei are calculated as

E(333.88) = 982*5301.04/13464 = 386.6326 etc

therefore,

$\chi ^{2}=279.9048$

df = (6-1)*(2-1) =5

P value is less than 0.0001

(the result is significant , reject H0)

Conclusion ;

We have sufficient evidence to conclude that there is a association between field of study and when study and when students enter college.