Question

a guidance counselor tracked college application outcomes for students with different gpa ranges. the two - way table shows incomplete data:

	accepted	rejected	total
gpa < 3.5		45	80
total	119

1. complete the two - way table by filling in all missing values.
2. how many students were accepted to college? how many total students applied?
3. among students with gpa ≥ 3.5, how many more were accepted than rejected?
4. compare the acceptance patterns between the two gpa groups. which group had more students accepted than rejected, and by how much?

Explanation:

Step1: Complete the two - way table

For the row "GPA ≥ 3.5", the number of rejected students is Total - Accepted. So, Rejected (GPA ≥ 3.5) = 120 - 84 = 36.
For the row "GPA < 3.5", the number of accepted students is Total - Rejected. So, Accepted (GPA < 3.5) = 80 - 45 = 35.
For the "Rejected" column total, it is 36+45 = 81.
For the "Total" row total, it is 120 + 80=200.
The completed table is:

	Accepted	Rejected	Total
GPA < 3.5	35	45	80
Total	119	81	200

Step2: Number of accepted students and total applicants

The number of accepted students is the total in the "Accepted" column, which is 119.
The total number of students who applied is the total of the "Total" row, which is 200.

Step3: Difference in accepted and rejected for GPA ≥ 3.5

For GPA ≥ 3.5, Accepted = 84, Rejected = 36. The difference is 84 - 36 = 48.

Step4: Compare acceptance patterns

For GPA ≥ 3.5: Accepted (84) > Rejected (36), difference is 84 - 36 = 48.
For GPA < 3.5: Accepted (35) < Rejected (45), difference (rejected - accepted) is 45 - 35 = 10.
So the group with GPA ≥ 3.5 had more students accepted than rejected, by 48.

Answer:

s:

1. The completed two - way table is as above.
2. The number of students accepted to college is 119. The total number of students who applied is 200.
3. Among students with GPA ≥ 3.5, the number of students who were accepted more than rejected is 48.
4. The group with GPA ≥ 3.5 had more students accepted than rejected. The group with GPA ≥ 3.5 had 48 more students accepted than rejected, while the group with GPA < 3.5 had more students rejected than accepted.