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  = .05. Factor A is method of loading and unloading; Factor B is the type of ride.

	Types of Rides
	Roller Coaster	Screaming Demon	Long Flume
Method 1	46	56	53
	48	48	49
Method 2	46	49	50
	48	45	46

a. Set up the ANOVA table (to 2 decimal, if necessary). Round p-value to four decimal places.

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

b. The p-value for Factor A is: less than .01 OR between .01 and .025 OR between .025 and .05 OR between .05 and .10 OR
greater than .10
   What is your conclusion with respect to Factor A?
   Factor A is significant
   Factor A is not significant

c. The p-value for Factor B is: less than .01 OR between .01 and .025 OR between .025 and .05 OR between .05 and .10 OR
greater than .10
   What is your conclusion with respect to Factor B?
Factor B is significant
   Factor B is not significant

d. The p-value for the interaction of factors A and B is: less than .01 OR between .01 and .025 OR between .025 and .05 OR
between .05 and .10 OR greater than .10
   What is your conclusion with respect to interaction of Factors A and B?
The interaction of factors A and B is significant
The interaction of factors A and B is not significant

e. What is your recommendation to the amusement park?
Use method 1; it has a lower sample mean waiting time and is the best method
   Withhold judgement; take a larger sample before making a final decision
   Since method is not a significant factor, use either loading and unloading method

Answer 1

a)

Using Exceldata -> data analysis -> Anova: Two-Factor With Replication

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
A	21.33333	1	21.33333	2.133333	0.194427	5.987378
B	16.66667	2	8.333333	0.833333	0.479329	5.143253
Interaction	12.66667	2	6.333333	0.633333	0.562922	5.143253
Within	60	6	10
Total	110.6667	11

if p-value < alpha, we reject the null hypothesis

if p-value > alpha, we fail to reject the null hypothesis

for b),c) and d)

all have p-value > 0.10

hence none of them are significant

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