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	43	52	48
	45	44	44
Method 2	47	50	50
	49	46	46

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 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.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 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 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 not 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.

2. You may need to use the appropriate technology to answer this question.

The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 282, SSA = 26, SSB = 22, SSAB = 179.Set up the ANOVA table. (Round your values for mean squares and F to two decimal places, and your p-values to three decimal places.)

Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
Factor A
Factor B
Interaction
Error
Total

Test for any significant main effects and any interaction effect. Use α = 0.05.

Find the value of the test statistic for factor A. (Round your answer to two decimal places.)

Find the p-value for factor A. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor A.

Because the p-value ≤ α = 0.05, factor A is not significant.Because the p-value ≤ α = 0.05, factor A is significant.     Because the p-value > α = 0.05, factor A is not significant.Because the p-value > α = 0.05, factor A is significant.

Find the value of the test statistic for factor B. (Round your answer to two decimal places.)

Find the p-value for factor B. (Round your answer to three decimal places.)

p-value =

State your conclusion about factor B.

Because the p-value ≤ α = 0.05, factor B is significant.Because the p-value ≤ α = 0.05, factor B is not significant.     Because the p-value > α = 0.05, factor B is not significant.Because the p-value > α = 0.05, factor B is significant.

Find the value of the test statistic for the interaction between factors A and B. (Round your answer to two decimal places.)

Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)

p-value =

State your conclusion about the interaction between factors A and B.

Because the p-value > α = 0.05, the interaction between factors A and B is not significant.Because the p-value ≤ α = 0.05, the interaction between factors A and B is not significant.     Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant.Because the p-value > α = 0.05, the interaction between factors A and B is significant.

Answer 1

1)

Source of Variation	SS	df	MS	F	P-value
method	12	1	12	1.2	0.315
type	8	2	4	0.4	0.687
Interaction	8	2	4	0.4	0.687
Within	60	6	10
Total	88	11

value of the test statistic for method of loading and unloading =1.2

p value =0.315

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

value of the test statistic for method of type of ride =0.4

p value =0.687

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

value of the test statistic for interaction between method of loading and unloading and type of ride is =0.4

p value =0.687

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

2)

Source	SS	df	MS	F	p vlaue
A	26	3	8.67	3.78	0.024
B	22	2	11.00	4.80	0.018
A*B	179	6	29.83	13.02	0.000
error	55	24	2.29
total	282	35

value of the test statistic for factor A =3.78

p value =0.024

.Because the p-value ≤ α = 0.05, factor A is significant.   

value of the test statistic for factor B =4.80

p value =0.018

.Because the p-value ≤ α = 0.05, factor B is significant.   

value of the test statistic for the interaction between factors A and B =13.02

p value =0.000

  Because the p-value ≤ α = 0.05, the interaction between factors A and B is significant