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.

	Type of Ride
	Roller Coaster	Screaming Demon	Long Flume
Method 1	42	55	52
	44	47	48
Method 2	47	50	51
	49	46	47

1. 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

   
   
2. The p-value for Factor A is Select:less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10
3. What is your conclusion with respect to Factor A? Select:Factor A is significant, Factor A is not significant
4. The p-value for Factor B is Select: less than .01, between .01 and .025 between .025 and .05, between .05 and .10, greater than .10
5. What is your conclusion with respect to Factor B?
   Select: Factor B is significant, Factor B is not significant
   
6. The p-value for the interaction of factors A and B is Select: less than .01, between .01 and .025, between .025 and .05, between .05 and .10, greater than .10
7. What is your conclusion with respect to the interaction of Factors A and B?
   Select: The interaction of factors A and B is significant, The interaction of factors A and B is not significantI
   
8. What is your recommendation to the amusement park?
   Select: Use method 1; it has a lower sample mean waiting time and is the best method, Withhold judgment; take a larger sample before making a final decision Since method is not a significant factor, use either loading and unloading method

Answer 1

Output using excel:

a)

Anova: Two-Factor With Replication
SUMMARY	Roller Coaster	Screaming Demon	Long Flume	Total
Method 1
Count	2	2	2	6
Sum	86	102	100	288
Average	43	51	50	48
Variance	2	32	8	23.6
Method 2
Count	2	2	2	6
Sum	96	96	98	290
Average	48	48	49	48.33333
Variance	2	8	8	3.866667
Total
Count	4	4	4
Sum	182	198	198
Average	45.5	49.5	49.5
Variance	9.666667	16.33333	5.666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	0.33	1	0.33	0.03	0.8611	5.987378
Factor B	42.67	2	21.33	2.13	0.1996	5.143253
Interaction	34.67	2	17.33	1.73	0.2546	5.143253
Error	60	6	10
Total	137.6667	11

b) The p-value for Factor A is greater than .10

c) Conclusion with respect to Factor A:

Factor A is not significant.

d) The p-value for Factor B is greater than .10

e) Conclusion with respect to Factor B:

Factor B is not significant.

f) The p-value for the interaction of factors A and B is greater than .10

g) Conclusion with respect to the interaction of Factors A and B:

The interaction of factors A and B is not significant.

h) Recommendation:

Withhold judgement: take a larger sample before making a final decision