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 a= 0.05 . 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	44	53	48
	46	45	44
Method 2	48	45	51
	50	41	47

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	1	1	1	0.1	0.75
Factor B		2
Interaction
Error
Total

Answer 1

Result:

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 a= 0.05 . 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	44	53	48
	46	45	44
Method 2	48	45	51
	50	41	47

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

Excel Addon Megastat used.

Two factor ANOVA
			FactorB
	Means:
		Roller Coaster	Screaming Demon	Long Flume
	Method 1	45.0	49.0	46.0	46.7
Factor A	Method 2	49.0	43.0	49.0	47.0
		47.0	46.0	47.5	46.8
	2	replications per cell
ANOVA table
Source	SS	df	MS	F	p-value
Factor A	0.33	1	0.333	0.03	.8611
Factor B	4.67	2	2.333	0.23	.7988
Interaction	60.67	2	30.333	3.03	.1229
Error	60.00	6	10.000
Total	125.67	11

To test the effect of Factor A, calculated F=0.03, P=0.8611 which is > 0.05 level of significance. Ho is not rejected. Factor A is not significant.

To test the effect of Factor B, calculated F=0.23, P=0.7988 which is > 0.05 level of significance. Ho is not rejected. Factor B is not significant.

To test the effect of interaction, calculated F=3.03, P=0.1229 which is > 0.05 level of significance. Ho is not rejected. Interaction is not significant.

( Note: report the results with required decimals)