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

ID: 3438195 • Letter: A

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 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 54 46 47 46 42 Method 2 44 48 52 46 44 48

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

Source of Variation Sum of Squares Degrees of Freedom Mean Square F Factor A Factor B Interaction Error Total

Explanation / Answer

Using excel we get the following result for two factor anova with replication:

( Go to 'Data----> Data Analysis-----> ANOVA : Two factor with replication-----> OK--->Input range(the whole table leaving the row of type of ride)----> rows per sample(2 as replication in each method is 2)----> OK

Hence p value for factor A is 0.86 which is greater than 0.10. If we test this at 5% level of significance than we can say p value is greater than alpha hence we cannot reject our null hypothesis and say there is not main effect of method 1 and 2. It means factor A is not significant.

p value for factor B = 0.56 which is greater than 0.10.

At 5% level of significance we can not reject null hypothesis and say that factor B is not significant.

The p-value for the interaction of factors A and B is 0.15 ,which is also greater than 0.10 , hence the interaction of factors A and B is not significant.

recommendation to the amusement park:

take a larger sample before making a final decision Since method is not a significant factor.

Anova: Two-Factor With Replication SUMMARY Roller Coaster Screaming Demon Long Flume Total Method 1 Count 2 2 2 6 Sum 92 100 88 280 Average 46 50 44 46.66667 Variance 2 32 8 15.86667 Method 2 Count 2 2 2 6 Sum 90 92 100 282 Average 45 46 50 47 Variance 2 8 8 9.2 Total Count 4 4 4 Sum 182 192 188 Average 45.5 48 47 Variance 1.666667 18.66667 17.33333 ANOVA Source of Variation SS df MS F P-value F crit Sample 0.333333 1 0.333333 0.033333 0.861145 5.987378 Columns 12.66667 2 6.333333 0.633333 0.562922 5.143253 Interaction 52.66667 2 26.33333 2.633333 0.151031 5.143253 Within 60 6 10 Total 125.6667 11

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

An amusement park, whose customer set is made up of two markets, adult and child

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

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