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 a=.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 40 56 48 42 48 44 Method 2 48 51 50 50 47 46 Set up the ANOVA table (to whole number, but p-value to 2 decimals and F value to 1 decimal, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A Factor B Interaction Error Total

Answer 1

Solution: We can use the excel Anova: Two-Factor With Replication to answer the given question. The excel output is given below:

Anova: Two-Factor With Replication
SUMMARY	Roller Coaster	Screaming Demon	Long Flume	Total
Method 1
Count	2	2	2	6
Sum	82	104	92	278
Average	41	52	46	46.33333
Variance	2	32	8	32.66667
Method 2
Count	2	2	2	6
Sum	98	98	96	292
Average	49	49	48	48.66667
Variance	2	8	8	3.866667
Total
Count	4	4	4
Sum	180	202	188
Average	45	50.5	47
Variance	22.66667	16.33333	6.666667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	16.33333	1	16.33333	1.633333	0.248457	5.987378
Columns	62	2	31	3.1	0.118953	5.143253
Interaction	60.66667	2	30.33333	3.033333	0.12294	5.143253
Within	60	6	10
Total	199	11

Therefore, the ANOVA can be filled as: