An amusement park studied methods for decreasing the waiting time (minutes) for

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.

Set up the ANOVA table (to 1 decimal, if necessary).

The p-value :

Factor A :

less than .01

between .01 and .025

between .025 and .05

between .05 and .10

greater than .10

What is your conclusion with respect to Factor A?
Factor A is significant or Factor A is not significantItem 19

The p-value for Factor B :

less than .01

between .01 and .025

between .025 and .05

between .05 and .10

greater than .10

What is your conclusion with respect to Factor B?
Factor B is significant or Factor B is not significantItem 21

The p-value for the interaction of factors A and B ?

less than .01

between .01 and .025

between .025 and .05

between .05 and .10

greater than .10

What is your conclusion with respect to the interaction of Factors A and B?
The interaction of factors A and B is significant or The interaction of factors A and B is not significantItem 23

What is your recommendation to the amusement park?
Use method 1; it has a lower sample mean waiting time and is the best method

or

Withhold judgment; take a larger sample before making a final decision

or

Since method is not a significant factor, use either loading and unloading methodItem 24

Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 40 50 47 42 42 43 Method 2 45 52 47 47 48 43

Explanation / Answer

applying two way ANOVA on above data:

The p-value :

Factor A : greater than .10

Factor A is not significant

The p-value for Factor B : greater than .10 Factor B is not significant

The p-value for the interaction of factors A and B : 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

SUMMARY Roller Coaster Screaming Demon Long Flume Total Method 1 Count 2 2 2 6 Sum 82 92 90 264 Average 41 46 45 44 Variance 2 32 8 14 Method 2 Count 2 2 2 6 Sum 92 100 90 282 Average 46 50 45 47 Variance 2 8 8 9.2 Total Count 4 4 4 Sum 174 192 180 Average 43.5 48 45 Variance 9.666667 18.66667 5.333333 ANOVA Source of Variation SS df MS F factor A 27 1 27 2.7 factor B 42 2 21 2.1 Interaction 14 2 7 0.7 error 60 6 10 Total 143 11

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