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 α = 0.05.

	Type of Ride
	Roller Coaster	Screaming Demon	Log Flume
Method 1	43	50	50
	45	42	46
Method 2	47	52	48
	49	48	44

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

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

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.

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 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.

Answer 1

Anova: Two-Factor With Replication
SUMMARY	Roller Coaster	Screaming Demon	Log Flume	Total
method 1
Count	2	2	2	6
Sum	88	92	96	276
Average	44	46	48	46
Variance	2	32	8	11.6
method 2
Count	2	2	2	6
Sum	96	100	92	288
Average	48	50	46	48
Variance	2	8	8	6.8
Total
Count	4	4	4
Sum	184	192	188
Average	46	48	47
Variance	6.666667	18.66667	6.666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
loading/unloading	12	1	12	1.2	0.315334	5.987378
type of ride	8	2	4	0.4	0.686953	5.143253
Interaction	24	2	12	1.2	0.364431	5.143253
Within	60	6	10
Total	104	11

F stat for loading/unlaoding = 1.2

p value = 0.315334

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

..........

F stat for ride = 0.4

p value = 0.686953

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

............

test statistic for interaction between method of loading and unloading and type of ride. = 1.2

p value = 0.364431

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

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