Question

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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 α = 0.05.

	Type of Ride
	Roller Coaster	Screaming Demon	Log Flume
Method 1	41	52	50
	43	44	46
Method 2	49	50	48
	51	46	44

Find the value of the test statistic for method of loading and unloading.

Find the p-value for method of loading and unloading. (Round your answer to three decimal places.)

p-value =

State your conclusion about method of loading and unloading.

Because the p-value ≤ α = 0.05, method of loading and unloading is significant.

Because the p-value ≤ α = 0.05, method of loading and unloading is not significant.  

  Because the p-value > α = 0.05, method of loading and unloading is significant.

Because the p-value > α = 0.05, method of loading and unloading is not significant.

Find the value of the test statistic for type of ride.

Find the p-value for type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about type of ride.

Because the p-value > α = 0.05, type of ride is not significant.

Because the p-value > α = 0.05, type of ride is significant.   

Because the p-value ≤ α = 0.05, type of ride is significant.

Because the p-value ≤ α = 0.05, type of ride is not significant.

Find the value of the test statistic for interaction between method of loading and unloading and type of ride.

Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.)

p-value =

State your conclusion about interaction between method of loading and unloading and type of ride.

Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is significant.

Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is not significant.  

  Because the p-value > α = 0.05, interaction between method of loading and unloading and type of ride is not significant.

Because the p-value ≤ α = 0.05, interaction between method of loading and unloading and type of ride is significant.

Answer 1

from excel: data -data analysis: 2 way ANOVA with replication:

Source of Variation	SS	df	MS	F	P-value
factor A	12	1	12	1.2	0.315
factor B	8	2	4	0.4	0.687
Interaction	56	2	28	2.8	0.138
Within	60	6	10
Total	136	11

value of test statistic for factor A =1.2

p value =0.315

because the p value >0.05 , factor A is not significant

value of test statistic for factor B =0.4

p value =0.687

because the p value >0.05 , factor B is not significant

value of test statistic for interaction =2.8

p value =0.138

because the p value >0.05 , interaction is not significant