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	43	55	50
	45	47	46
Method 2	45	47	48
	47	43	44

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

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

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

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

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 method

Answer 1

applying 2 way ANOVA on above:

Source of Variation	SS	df	MS	F	P-value
factor A	12	1	12	1.2	0.3153
factor B	18.67	2	9.34	0.93	0.4437
Interaction	32	2	16	1.6	0.2774
Within	60	6	10
Total	122.6667	11

The p-value for Factor A is  greater than .10

Factor A is not significant

The p-value for Factor B is  greater than .10

Factor B is not significant

p-value for the interaction of factors A and B is  greater than .10

interaction of factors A and B is  not significant

Since method is not a significant factor, use either loading and unloading method