Homework SourseExercise 1331 Algorithmic An amusement park studied methods
{Exercise 13.31 (Algorithmic)}
An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use = .05. Factor A is method of loading and unloading; Factor B is the type of ride.
Set up the ANOVA table (to 1 decimal, if necessary).
The p-value for Factor A is
What is your conclusion with respect to Factor A?
The p-value for Factor B is
What is your conclusion with respect to Factor B?
The p-value for the interaction of factors A and B is
What is your conclusion with respect to the interaction of Factors A and B?
What is your recommendation to the amusement park?
| Type of Ride | |||
| Roller Coaster | Screaming Demon | Long Flume | |
| Method 1 | 45 | 52 | 49 |
| 47 | 44 | 45 | |
| Method 2 | 50 | 54 | 48 |
| 52 | 50 | 44 |
Solution
An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use = .05. Factor A is method of loading and unloading; Factor B is the type of ride.
Type of Ride
Roller Coaster
Screaming Demon
Long Flume
Method 1
45
52
49
47
44
45
Method 2
50
54
48
52
50
44
Set up the ANOVA table (to 1 decimal, if necessary).
Two factor ANOVA
Factor B
Means:
Roller Coaster
Screaming Demon
Long Flume
Method 1
46.0
48.0
47.0
47.0
Factor A
Method 2
51.0
52.0
46.0
49.7
48.5
50.0
46.5
48.3
2
replications per cell
ANOVA table
Source
SS
df
MS
F
p-value
Factor A
21.33
1
21.333
2.13
.1944
Factor B
24.67
2
12.333
1.23
.3559
Interaction
20.67
2
10.333
1.03
.4115
Error
60.00
6
10.000
Total
126.67
11
The p-value for Factor A is 0.1944
Calculated P=0.1944 > 0.05 level. The null hypothesis is not rejected.
What is your conclusion with respect to Factor A?
Factor A is not significant.
The p-value for Factor B is 0.3559
Calculated P=0.3559 > 0.05 level. The null hypothesis is not rejected.
What is your conclusion with respect to Factor B?
Factor B is not significant.
The p-value for the interaction of factors A and B is 0.4115
Calculated P=0.4115 > 0.05 level. The null hypothesis is not rejected.
What is your conclusion with respect to the interaction of Factors A and B?
Interaction is not significant.
What is your recommendation to the amusement park?
We conclude that there is no significant effect due to the loading and unloading method, the type of ride, and interaction.
| Type of Ride | |||
| Roller Coaster | Screaming Demon | Long Flume | |
| Method 1 | 45 | 52 | 49 |
| 47 | 44 | 45 | |
| Method 2 | 50 | 54 | 48 |
| 52 | 50 | 44 |
