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=0.5. 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	41	51	47
	43	43	43
Method 2	46	51	47
	48	47	43

Set up the ANOVA table (to whole number, butp -value to 2 decimals and f 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 p-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 p-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?

Answer 1

The R code and the results are given as follows:

> y<-c(41, 43, 46, 48, 51, 43, 51, 47, 47, 43, 47, 43) > A<-c(1, 1, 2, 2, 1, 1, 2, 2,1, 1, 2, 2) > B<-c(1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3) > A<-as.factor(A) > B<-as.factor(B) > results<-lm(y~A*B) > anova(results) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) A 1 16.333 16.3333 1.6333 0.2485 B 2 28.667 14.3333 1.4333 0.3099 A:B 2 12.667 6.3333 0.6333 0.5629 Residuals 6 60.000 10.0000

So, here we can see that none of the factors and their interaction are significant at 0.1, 0.05 level.