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	46	54	50
	48	46	46
Method 2	45	54	48
	47	50	44

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>Anova with replication

we have

Anova: Two-Factor With Replication
SUMMARY	Roller Coaster	Screaming Demon	Long Flume	Total
Method 1
Count	2	2	2	6
Sum	94	100	96	290
Average	47	50	48	48.33333
Variance	2	32	8	10.26667
Method 2
Count	2	2	2	6
Sum	92	104	92	288
Average	46	52	46	48
Variance	2	8	8	13.2
Total
Count	4	4	4
Sum	186	204	188
Average	46.5	51	47
Variance	1.666667	14.66667	6.666667
ANOVA
Source of Variation	SS	df	MS	F	P-value
Factor A	0.333333	1	0.333333	0.033333	0.861145
Factor B	48.66667	2	24.33333	2.433333	0.168331
Interaction	8.666667	2	4.333333	0.433333	0.667138
Within	60	6	10
Total	117.6667	11