Question

Please use exact data provided here in this 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 48 55 49 50 47 45 Method 2 48 45 50 50 41 46 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 What is your conclusion with respect to Factor A? The p-value for Factor B is What is your conclusion with respect to Factor B? The p-value for the interaction of factors A and B is What is your conclusion with respect to the interaction of Factors A and B? What is your recommendation to the amusement park?

Answer 1

Solution:

Two factor ANOVA
			Factor 2
	Means:
		Column 1	Column 2	Column 3
	Row 1	49.0	51.0	47.0	49.0
Factor 1	Row 2	49.0	43.0	48.0	46.7
		49.0	47.0	47.5	47.8
	2	replications per cell
ANOVA table
Source	SS	df	MS	F	p-value
Factor 1	16.33	1	16.333	1.63	.2485
Factor 2	8.67	2	4.333	0.43	.6671
Interaction	48.67	2	24.333	2.43	.1683
Error	60.00	6	10.000
Total	133.67	11

The p-value of Factor A is 0.2485. Since p-value is greater than 0.05 level of significance, we fail to reject Ho. Hence, factor A is not significant.

The p-value of Factor B is 0.6671. Since p-value is greater than 0.05 level of significance, we fail to reject Ho.Hence, factor B is not significant.

The p-value of interaction of Factor A and Factor B is 0.1683. Since p-value is greater than 0.05 level of significance, we fail to reject Ho.Hence, interaction of factor A and factor B is not significant.