Question

A survey of 13,364 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	942	34%	66%
Design	584	47%	53%
Health	5085	40%	60%
Media/IT	3148	31%	69%
Service	1350	36%	64%
Other	2255	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.

The survey also asked about how these college students paid for their education. A major source of funding was government loans. Here are the survey percents of private students in the country who use government loans to finance their education by field of study.

Field of Study	Number of Students	Percent Using Government Loans
Trades	942	45%
Design	589	53%
Health	5234	55%
Media/IT	3248	55%
Service	1378	60%
Other	2320	47%

(a) Construct the 6 ✕ 2 table of counts for this exercise.

		Using Government Loans
Field of Study		Yes		No
Trades
Design
Health
Media/IT
Service
Other

(b) Test the null hypothesis that the percent of students using government loans to finance their education does not vary with field of study. Be sure to provide all the details of your significance test. (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 taking government loans.

    

H₀: There is an association between number of students and taking government loans.

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 taking government loans.

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 taking government loans.

    

H_a: There is an association between number of students and taking government loans.

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 taking government loans.

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	=

(c) Summarize your analysis and conclusions.

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 taking government loans.

We have sufficient evidence to conclude that there is an association between number of students and taking government loans.

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 taking government loans.

(d) The number of students reported in this exercise is not the same as the number reported in the first table. Suggest a possible reason for this difference.

Answer 1