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	45	51	53
	47	43	49
Method 2	47	55	48
	49	51	44

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?

Answer 1

The Cell means are as below

	RC	SD	LF	Total
Method 1	92	104	102	298
Method 2	96	106	92	294
Total	188	210	194	592

(a) The ANOVA Table is as below

	SS	df	MS	F	F critical	P value
A - Rows	1.33	1	1.33	0.27	5.99	0.6219
B - columns	64.67	2	32.34	6.47	5.14	0.0318
A x B	28.67	2	14.34	2.87	5.14	0.1335
Error	30.00	6	5.00
Total	124.67	11

For (b), (c) and (d), if p value is < 0.05, the result is significant (we reject the null hypothesis in favor of the alternative)

______________________________________

(b) The p value for A is greater than 0.10

Factor A is not significant

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(c) The p value for B is between 0.025 and 0.05

Factor B is significant

________________________________________

(d) The p value for Interaction is greater than 0.10

Interaction of Factors A and B is not significant

________________________________________

(e) Recommendation: Since method is not significant, we can use either method 1 or 2.

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