A survey of 13,414 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 Number of Time of Entry
Study Students
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 5294 55%
Media/IT 3218 55%
Service 1368 60%
Other 2360 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: (Choose one of the statements)
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.