Question

In: Statistics and Probability

A survey of 13,364 students in a country who enrolled in private career colleges was conducted...

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:

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

Ha: There is an association between field of study and taking government loans.

    

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

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

Ha: 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.

Solutions

Expert Solution

orchestra answered 1 year ago
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