Question

Because of the high cost of hiring and training new employees, employers would like to ensure that they retain highly qualified workers. To help develop a hiring program, the human resources manager of a large company wanted to compare how long business and non-business university graduates worked for the company before quitting to accept a position elsewhere. The manager selected a random sample of 25 business and 20 nonbusiness graduates who had been hired 5 years ago. The number of months each employee 3 had worked for the company was recorded. (Those who had not quit were recorded as having worked for 60 months.) Is the average duration of employment the same for business and non-business graduates before quitting to accept a position elsewhere?

a) Are the samples independent? What is the appropriate parametric test here? Draw the histograms of duration of employment for business and non-business graduates and comment on the justification of using/not using a parametric test here to address the question of interest.

b) Use an appropriate non-parametric test to compare the average duration of employment of business and non-business graduates at 5% level of significance. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.

Business	Non-Bus
60	25
11	60
18	22
19	24
5	23
25	36
60	39
7	15
8	35
17	16
37	28
4	9
8	60
28	29
27	16
11	22
60	60
25	17
5	60
13	32
22
11
17
9
4

Answer 1

a) Are the samples independent? What is the appropriate parametric test here? Draw the histograms of duration of employment for business and non-business graduates and comment on the justification of using/not using a parametric test here to address the question of interest.

The samples are independent. The appropriate parametric test is the two-sample independent t-test.

The histograms are:

Since the data is not normally distributed, we cannot use a parametric test.

b) Use an appropriate non-parametric test to compare the average duration of employment of business and non-business graduates at 5% level of significance. Make sure you follow all the steps for hypothesis testing indicated in the Instructions section and show your computations.

η₁: median of Business

η₂: median of Non-Bus

Difference: η₁ - η₂

Descriptive Statistics

Sample	N	Median
Business	25	17.0
Non-Bus	20	26.5

Estimation for Difference

Difference	CI for Difference	Achieved Confidence
-11	(-19, -3)	95.18%

Test

Null hypothesis	H₀: η₁ - η₂ = 0
Alternative hypothesis	H₁: η₁ - η₂ ≠ 0

Method	W-Value	P-Value
Not adjusted for ties	463.00	0.011
Adjusted for ties	463.00	0.011

Since the p-value (0.011) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that there is a difference between the average duration of employment of business and non-business graduates.