{Exercise 13.31 (Algorithmic)} An amusement park studied methods for decreasing
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Question
{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.
{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.
Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 46 52 51 48 44 47 Method 2 45 52 51 47 48 47- Set up the ANOVA table (to 1 decimal, if necessary).
Source of Variation Sum of Squares Degrees of Freedom Mean Square F Factor A Factor B Interaction Error Total - The p-value for Factor A is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 18
What is your conclusion with respect to Factor A?
SelectFactor A is significantFactor A is not significantItem 19 - The p-value for Factor B is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 20
What is your conclusion with respect to Factor B?
SelectFactor B is significantFactor B is not significantItem 21 - The p-value for the interaction of factors A and B is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 22
What is your conclusion with respect to the interaction of Factors A and B?
SelectThe interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 23 - What is your recommendation to the amusement park?
SelectUse method 1; it has a lower sample mean waiting time and is the best methodWithhold judgment; take a larger sample before making a final decisionSince method is not a significant factor, use either loading and unloading methodItem 24
Explanation / Answer
from above:
The p-value for Factor A is greater than 0.10
Factor A is not significant
The p-value for Factor B is greater than 0.10
Factor B is not significant
The p-value for the interaction of factors A and B is greater than 0.10
The interaction of factors A and B is not significant
Since method is not a significant factor, use either loading and unloading method
SUMMARY Roller Coaster Screaming Demon Long Flume Total Method 1 Count 2 2 2 6 Sum 94 96 98 288 Average 47 48 49 48 Variance 2 32 8 9.2 Method 2 Count 2 2 2 6 Sum 92 100 98 290 Average 46 50 49 48.333333 Variance 2 8 8 7.0666667 Total Count 4 4 4 Sum 186 196 196 Average 46.5 49 49 Variance 1.666666667 14.66666667 5.333333333 ANOVA Source of Variation SS df MS F P-value F crit Factor A 0.3333 1 0.3333 0.0333 0.8611 5.9874 Factor B 16.6667 2 8.3333 0.8333 0.4793 5.1433 Interaction 4.6667 2 2.3333 0.2333 0.7988 5.1433 Error 60 6 10 Total 81.6667 11Related Questions
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