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 . 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	46	54	50
	48	46	46
Method 2	45	54	48
	47	50	44

Set up the ANOVA table (to whole number, but -value to 2 decimals and  value to 1 decimal, if necessary).

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

The -value for Factor A is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 21

What is your conclusion with respect to Factor A?

- Select your answer -Factor A is significantFactor A is not significantItem 22

The -value for Factor B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 23

What is your conclusion with respect to Factor B?

- Select your answer -Factor B is significantFactor B is not significantItem 24

The -value for the interaction of factors A and B is - Select your answer -less than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 25

What is your conclusion with respect to the interaction of Factors A and B?

- Select your answer -The interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 26

What is your recommendation to the amusement park?

- Select your answer -Use method 1; it has a lower sample mean waiting time and is the best methodWithhold judgment; take a larger sample before making a final decisionSince method is not a significant factor, use either loading and unloading methodItem 27

Answer 1

we used technology (R-software) to get the ANOVA table of given data and it as below:

Source of Variation	Degrees of Freedom	Sum of Squares	Mean Square	F value	p-value
Factor A(type of ride)	2	48.667	24.3333	2.4333	0.1683
Factor B(method)	1	0.333	0.3333	0.0333	0.8611
Interaction	2	8.667	4.3333	0.4333	0.6671
Error	6	60	10
Total	11	117.667

Based on the ANOVA table we can answer the given questions:

Answer(1): The p-value for Factor A is greater than 0.10

Conclusion: Factor A is not significant

Answer(2): The p-value for Factor B is greater than 0.10

Conclusion: Factor B is not significant

Answer(3): The p-value for interaction of factors A and B is greater than 0.10

Conclusion: The interaction of factors A and B is not significant

Answer(4): Recommendation to the amusement park

Take a larger sample before making a final decisionSince method is not a significant factor

I hope I have given satisfactory answers, If you have any doubt please ask in comment section.