Question

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	44	56	45
	46	48	41
Method 2	49	52	50
	51	48	46

1. Set up the ANOVA table (to 2 decimal, if necessary). Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Factor A
   Factor B
   Interaction
   Error
   Total

   
   
2. The p-value for Factor A is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 21
   
   What is your conclusion with respect to Factor A?
   SelectFactor A is significantFactor A is not significantItem 22
   
3. The p-value for Factor B is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 23
   
   What is your conclusion with respect to Factor B?
   SelectFactor B is significantFactor B is not significantItem 24
   
4. 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 25
   
   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 26
   
5. 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 27

Answer 1

For the given data using Anova: Two-Factor With Replication in Excel we get output as

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	21.33333	1	21.33333	2.133333	0.194427	5.987378
Columns	62	2	31	3.1	0.118953	5.143253
Interaction	32.66667	2	16.33333	1.633333	0.271446	5.143253
Within	60	6	10
Total	176	11

So from the above output