Question

A survey of 13,234 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.

Field of Study	Number of Students	Time of Entry
		Right After High School	Later
Trades	992	34%	66%
Design	564	47%	53%
Health	5035	40%	60%
Media/IT	3118	31%	69%
Service	1310	36%	64%
Other	2215	52%	48%

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 ✕ 2 table of counts for this problem.

		Time of Entry
Field of Study		Right After High School		Later
Trades
Design
Health
Media/IT
Service
Other

(b) Analyze the data. (Round your numerical answers to one decimal place.)

The most popular field of study is  ---Select--- Trades Design Health Media/IT Service Other  with   % of these students. The least popular field of study is  ---Select--- Trades Design Health Media/IT Service Other  with   % of these students. Overall   % of these students enrolled right after high school.

(c) Write a summary of your conclusions. Be sure to include the results of your significance testing. (Use α = 0.01.)

State the null and alternative hypotheses.

Null Hypothesis:

H₀: There is an association between field of study and number of students.

H₀: There is an association between field of study and when students enter college.

    

H₀: There is an association between when students enter college and number of students.

H₀: There is not an association between field of study and number of students.

H₀: There is not an association between field of study and when students enter college.

Alternative Hypothesis:

H_a: There is an association between field of study and number of students.

H_a: There is an association between field of study and when students enter college.

    

H_a: There is an association between when students enter college and number of students.

H_a: There is not an association between field of study and number of students.

H_a: There is not an association between field of study and when students enter college.

State the χ² statistic, degrees of freedom, and the P-value. (Round your answer for χ² to one decimal place and your P-value to four decimal places.)

χ2	=
df	=
P-value	=

Conclusion:

We have sufficient evidence to conclude that there is an association between field of study and number of students.

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

  We have sufficient evidence to conclude that there is an association between when students enter college and number of students.

We do not have sufficient evidence to conclude that there is an association between field of study and number of students.

We do not have sufficient evidence to conclude that there is an association between field of study and when students enter college.

Answer 1

a)

Oi	right after	later
Trades	337	655
Design	265	299
Health	2014	3021
Media/IT	967	2151
Service	472	838
Other	1152	1063

b)

The most popular field of study is   Health r  with   38.0% of these students. The least popular field of study is Design

with 4.3 % of these students. Overall 39.3 % of these students enrolled right after high school.

c)

H₀: There is not an association between field of study and when students enter college.

H_a: There is an association between field of study and when students enter college.

X² =272.410

df=5

p value =0.0000

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