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.

The p-value for Factor A is (Pick one): 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? (Pick one)
Factor A is significant / Factor A is not significant

The p-value for Factor B is (Pick one): 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? (Pick one)
Factor B is significant / Factor B is not significant

The p-value for the interaction of factors A and B is (Pick one): 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? (Pick one)
The interaction of factors A and B is significant / The interaction of factors A and B is not significant

What is your recommendation to the amusement park? (Pick one)

A) Use method 1; it has a lower sample mean waiting time and is the best method

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

C) Since method is not a significant factor, use either loading and unloading method

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.

Type of Ride Roller Coaster Screaming Demon Long Flume Method 1 43 51 55 45 43 51 Method 2 47 46 48 49 42 44 Set up the ANOVA table (to 1 decimal, if necessary). Round p-value to four decimal places.
Source of Variation Sum of Squares Degrees of Freedom Mean Square F p-value Factor A (BLANK) (BLANK) (BLANK) (BLANK) (BLANK) Factor B (BLANK) (BLANK) (BLANK) (BLANK) (BLANK) Interaction (BLANK) (BLANK) (BLANK) (BLANK) (BLANK) Error (BLANK) (BLANK) (BLANK) Total (BLANK) (BLANK) *Please fill in blanks

The p-value for Factor A is (Pick one): 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? (Pick one)
Factor A is significant / Factor A is not significant

The p-value for Factor B is (Pick one): 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? (Pick one)
Factor B is significant / Factor B is not significant

The p-value for the interaction of factors A and B is (Pick one): 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? (Pick one)
The interaction of factors A and B is significant / The interaction of factors A and B is not significant

What is your recommendation to the amusement park? (Pick one)

A) Use method 1; it has a lower sample mean waiting time and is the best method

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

C) Since method is not a significant factor, use either loading and unloading method

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

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

The interaction of factors A and B is not significant

C) Since method is not a significant factor, use either loading and unloading method

Source of Variation SS df MS F P-value factor A 12.00 1 12.00 1.20 0.3153 factor B 38.00 2 19.00 1.90 0.2295 Interaction 62.00 2 31.00 3.10 0.1190 error 60.00 6 10.00 Total 172.00 11

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