{Exercise 13.31 (Algorithmic)} An amusement park studied methods for decreasing

Question

{Exercise 13.31 (Algorithmic)}

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.

Set up the ANOVA table (to 2 decimal, if necessary).

The p-value for Factor A is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 18

What is your conclusion with respect to Factor A?
SelectFactor A is significantFactor A is not significantItem 19

The p-value for Factor B is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 20

What is your conclusion with respect to Factor B?
SelectFactor B is significantFactor B is not significantItem 21

The p-value for the interaction of factors A and B is Selectless than .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 22

What is your conclusion with respect to the interaction of Factors A and B?
SelectThe interaction of factors A and B is significantThe interaction of factors A and B is not significantItem 23

What is your recommendation to the amusement park?
SelectUse 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 24

Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 45 53 52 47 45 48 Method 2 45 50 51 47 46 47

Explanation / Answer

applying two way ANOVA on above data:

p-value for Factor A is greater than .10

Factor A is not significant

p-value for Factor B is greater than .10

Factor B is not significant

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

The interaction of factors A and B is not significant

since method is not a significant factor, use either loading and unloading method

Source of Variation SS df MS F P-value factor A 1.33 1 1.33 0.13 0.7275 factor B 26.00 2 13.00 1.30 0.3396 Interaction 0.67 2 0.33 0.03 0.9674 error 60.00 6 10.00 Total 88 11

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