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	51	47
	43	43	43
Method 2	46	49	47
	48	45	43

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

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

Answer 1

using excel>data >data analysis>two way ANOVA with replication

we have

SUMMARY	Roller Coaster	Screaming Demon	Long Flume	Total
Method 1
Count	2	2	2	6
Sum	84	94	90	268
Average	42	47	45	44.66667
Variance	2	32	8	13.46667
Method 2
Count	2	2	2	6
Sum	94	94	90	278
Average	47	47	45	46.33333
Variance	2	8	8	4.666667
Total
Count	4	4	4
Sum	178	188	180
Average	44.5	47	45
Variance	9.666667	13.33333	5.333333
ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	8	1	8	0.8	0.40
Factor B	14	2	7	0.7	0.53
Interaction	17	2	9	0.8	0.48
Within	60	6	10
Total	99	11