Assignment:
The president of a large accounting firm is required to send employees back to school each year to catch up on the latest changes to tax laws. Each employee is sent to a two-week school and then must pass a competency exam showing that they have learned what they need to know. The president, although realizing the need for ongoing education, has long complained that sending employees away for two weeks is unproductive. Finally, after years of suffering, he sets out to find a better way of educating the employees. He soon discovers that several institutions are offering online versions of the required courses and exclaims: "This is perfect! Now, my employees can work all day and then study online at night. It's the best of both worlds."
While describing his plan to the accounting managers, one of the senior accountants asks the president if the quality of the online schools is equal that of the traditional schools. "After all," she says, "how do we know what we're getting? Maybe we should investigate this a little further before we commit all of our accountants to this plan". The president sees the validity of her argument and comes up with a plan. "I know what we'll do. Let's randomly choose half of our accountants to take the courses online and the other half can go to the regular schools. Once they come back, we'll see how the two groups compare on the competency examination". The company immediately goes about setting their plan into action!
1. What is the hypothesis that the company is investigating? Before they commit all their accountants to enroll in an online tax school, the company wants to find out if the quality of education for an online school is equal to traditional schools.
2. What is the independent variable? What are the levels of the independent variables? The independent variable is the time the accountants spend on studying. Traditionally, if the accountants are away from work for two weeks they have more time studying for the exam versus the accountants who must work all day and then log on at home, spending only a few hours of study time.
3. What is the dependent variable? The dependent variable are the scores the accountants receive on the company's competency exam.
4. Which statistical test would the company use to test their hypothesis?
5. For each of the sets of output below, what can you tell about the dependent variable? What decision would the president make?
Case One:
|
Variable
|
Group
|
# in Group
|
Mean
|
Standard Dev
|
Standard Error
|
|
Score
|
Online
|
10
|
84.10
|
5.2377
|
1.6563
|
|
|
Traditional
|
10
|
79.20
|
3.3267
|
1.0520
|
|
|
Levene Test
|
t-test for the Equality of Means
|
|
Score
|
F Value
|
p Value
|
t Value
|
Degrees of Freedom
|
1-tailed p Value
|
2-tailed p Value
|
|
Equal Variances Assumed
|
2.700
|
.188
|
2.497
|
18
|
.011
|
.022
|
|
Equal Variances Not Assumed
|
|
|
2.497
|
15.245
|
.012
|
.024
|
Case Two:
|
Variable
|
Group
|
# in Group
|
Mean
|
Standard Dev
|
Standard Error
|
|
Score
|
Online
|
10
|
84.10
|
5.2377
|
1.6563
|
|
|
Traditional
|
10
|
84.30
|
2.4518
|
0.7753
|
|
|
Levene Test
|
t-test for the Equality of Means
|
|
Score
|
F Value
|
p Value
|
t Value
|
Degrees of Freedom
|
1-tailed p Value
|
2-tailed p Value
|
|
Equal Variances Assumed
|
7.20
|
.015
|
.109
|
18
|
.4570
|
.914
|
|
Equal Variances Not Assumed
|
|
|
.109
|
12.763
|
.4575
|
.915
|
Case Three:
|
Variable
|
Group
|
# in Group
|
Mean
|
Standard Dev
|
Standard Error
|
|
Score
|
Online
|
10
|
84.10
|
5.2377
|
1.6563
|
|
|
Traditional
|
10
|
93.30
|
1.8288
|
.5783
|
|
|
Levene Test
|
t-test for the Equality of Means
|
|
Score
|
F Value
|
p Value
|
t Value
|
Degrees of Freedom
|
1-tailed p Value
|
2-tailed p Value
|
|
Equal Variances Assumed
|
10.32
|
.005
|
5.244
|
18
|
.000
|
.000
|
|
Equal Variances Not Assumed
|
|
|
5.244
|
11.162
|
.000
|
.000
|