Many college instructors prefer to have their students participate actively in c
ID: 3233231 • Letter: M
Question
Many college instructors prefer to have their students participate actively in class. Ideally, students will ask their professor questions and answer their professor's questions, making the classroom experience more interesting and useful. A statistics professor believes that there are a number of external factors that affect student participation. He believes that the time of day and the configuration of seats are two such factors. Consequently, he organized the following experiment. Six classes of about 60 students each were scheduled for one semester. Two classes were scheduled at 9:00 AM, two at 1:00 PM, and two at 4:00 PM. At each of the three times, one of the classes was assigned to a room where the seats were arranged in rows of 10 seats. The other class was a U-shaped, tiered room, where students not only face the instructor, but face their fellow students as well. In each of the six classrooms, over five days, student participation was measured by counting the number of times students asked and answered questions. These data are displayed in the accompanying table. (Xr14-97)
PART 1: How many factors are there in this experiment?
PART 2: What are the factors?
PART 3: What is the response variable?
PART 4: Identify the levels of each factor.
PART 5: What conclusions can the professor draw from these data?
Class 9:00am 1:00pm 4:00pm Rows 10 9 7 Rows 7 12 12 Rows 9 12 9 Rows 6 14 20 Rows 8 8 7 U-Shape 15 4 7 U-Shape 18 4 4 U-Shape 11 7 9 U-Shape 13 4 8 U-Shape 13 6 7Explanation / Answer
Answer:
Many college instructors prefer to have their students participate actively in class. Ideally, students will ask their professor questions and answer their professor's questions, making the classroom experience more interesting and useful. A statistics professor believes that there are a number of external factors that affect student participation. He believes that the time of day and the configuration of seats are two such factors. Consequently, he organized the following experiment. Six classes of about 60 students each were scheduled for one semester. Two classes were scheduled at 9:00 AM, two at 1:00 PM, and two at 4:00 PM. At each of the three times, one of the classes was assigned to a room where the seats were arranged in rows of 10 seats. The other class was a U-shaped, tiered room, where students not only face the instructor, but face their fellow students as well. In each of the six classrooms, over five days, student participation was measured by counting the number of times students asked and answered questions. These data are displayed in the accompanying table. (Xr14-97)
PART 1: How many factors are there in this experiment?
2 factors
PART 2: What are the factors?
Time of day and the configuration of seats are the two factors
PART 3: What is the response variable?
The number of times students asked and answered questions
PART 4: Identify the levels of each factor.
Class: 2 levels.
Time: 3 levels
PART 5: What conclusions can the professor draw from these data?
Two factor ANOVA
Factor 2
Means:
9:00am
1:00pm
4:00pm
Rows
8.0
11.0
11.0
10.0
Factor 1
U-Shape
14.0
5.0
7.0
8.7
11.0
8.0
9.0
9.3
5
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1
13.33
1
13.333
1.58
.2203
Factor 2
46.67
2
23.333
2.77
.0826
Interaction
206.67
2
103.333
12.28
.0002
Error
202.00
24
8.417
Total
468.67
29
To test for class effect, calculated F=1.58, P=0.2203 which is > 0.05 level. Ho is not rejected.
There is no significant class effect.
To test for time effect, calculated F=2.77, P=0.0826 which is > 0.05 level. Ho is not rejected.
There is no significant time effect.
To test for interaction effect, calculated F=12.28, P=0.0002 which is < 0.05 level. Ho is rejected.
There is significant interaction effect.
Two factor ANOVA
Factor 2
Means:
9:00am
1:00pm
4:00pm
Rows
8.0
11.0
11.0
10.0
Factor 1
U-Shape
14.0
5.0
7.0
8.7
11.0
8.0
9.0
9.3
5
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor 1
13.33
1
13.333
1.58
.2203
Factor 2
46.67
2
23.333
2.77
.0826
Interaction
206.67
2
103.333
12.28
.0002
Error
202.00
24
8.417
Total
468.67
29
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