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	45	52	46
	47	44	42
Method 2	45	50	52
	47	46	48

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

Anova: Two-Factor With Replication
SUMMARY	Roller Coaster	Screaming Demon	Long Flume	Total
Method 1
Count	2	2	2	6
Sum	92	96	88	276
Average	46	48	44	46
Variance	2	32	8	11.6
Method 2
Count	2	2	2	6
Sum	92	96	100	288
Average	46	48	50	48
Variance	2	8	8	6.8
Total
Count	4	4	4
Sum	184	192	188
Average	46	48	47
Variance	1.333333	13.33333	17.33333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	12	1	12	1.2	0.315334	5.987378
Factor B	8	2	4	0.4	0.686953	5.143253
Interaction	24	2	12	1.2	0.364431	5.143253
Error	60	6	10
Total	104	11

Test statistic for method of loading and unloading:

p-value = 0.315

Conclusion:

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

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Test statistic for type of ride.

p-value = 0.687

Conclusion:

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

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Test statistic for interaction between method of loading and unloading and type of ride.

p-value = 0.364

Conclusion:

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