Question

1. There are two career fairs held at a Catholic Chicago University.

Career Fair	Attendees	Hired	Not Hired
Fall	1000	150
Spring	600	120

1. Fill in the not-hired counts for each fair.

2. Do the samples meet the Success-Failure Conditions?

3. What are the proportions of hired students for each fair?

4. What are the individual standard errors for hired students?

5. What is the difference of proportions of hired students between the two fairs?

6. What is the joint standard error of the two fairs?

7. What is the z-score associated with 90 confidence interval?

8. Compute the confidence interval for this difference of proportions.

1. Which fair should a student attend?

Answer 1

(a)

The not-hired counts for each fair is filled up as follows:

Career Fair	Attendees	Hired	Not Hired
Fall	1000	150	850
Spring	600	120	480

(b)

Sample 1:

n1 = 1000

1 = 150/1000 = 0.15

n1 1 = 1000 X 0.15 = 150 10

n1 (1 - 1) =1000 X 0.85 = 850 10

Sample 2:

n2 = 600

2 = 120/600 = 0.20

n1 2 = 600 X 0.20 = 120 10

n1 (1 - 2) =600 X 0.80 = 480 10

So,

the samples meet the Success-Failure Conditions

(c)

For Fall:

the proportions of hired students = 1 = 150/1000 = 0.15

For Spring:

the proportions of hired students = 2 = 120/600 = 0.20

(d)

For Fall:

For pring:

(e)

the difference of proportions of hired students between the two fairs = 0.15 - 0.20 = - 0.05

(f)

the joint standard error of the two fairs is given by:

(g)

the z-score associated with 90 confidence interval = 1.645

(h)

Confidence Interval:

So,

Anwer is:

(-0.083,-0.017)

(i)

The student should attend Spring Fair becuae is has more proportions of hired students.