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 . 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	41	50	53
	43	42	49
Method 2	48	51	50
	50	47	46

Set up the ANOVA table (to whole number, but p-value to 2 decimals and F value to 1 decimal, if necessary).

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

Answer 1

From the given data,

			Factor B
			Roller Coaster	Screaming Demon	Long Flume	Row Total
Factor A	Method 1	Mean	42	46	51
Total	84	92	102	278
SS	2	32	8
Method 2	Mean	49	49	48
Total	98	98	96	292
SS	2	8	8
		Col Total:	182	190	198	570

ANOVA Table;

ANOVA Table		SS	df	MSS	F-Ratio	F-crit
SSbetween treatment		99.0000	5.0000	19.8000
SS row	A	16.3333	1.0000	16.3333	1.6333	5.9874
SS col	B	32.0000	2.0000	16.0000	1.6000	5.1433
SS row*col	A*B	50.6667	2.0000	25.3333	2.5333	5.1433
Within treatment		60.0000	6.0000	10.0000
Total :		159.0000	11.0000