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 . 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	42	54	46
	44	46	42
Method 2	47	53	49
	49	49	45

Set up the ANOVA table (to whole number, but -value to 2 decimals and 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

Answer 1

Solution:

It is a case of two way ANOVA with replication. we can perform ANOVA using EXCEL which is as follows.

Step to perform 2 way ANOVA with replication

• Enter the data into the worksheet
• DATA > Data Analysis > ANOVA: two factors with replication
• Select the Data into Input Range:
• Choose Rows per sample: 2 (2-row replicate for method 1 and method 2 each)
• Click OK on each dialogue box.

The Excel output is as follows:

ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	8	1	8	0.571429	0.491767	7.708647
Columns	50	1	50	3.571429	0.131778	7.708647
Interaction	2	1	2	0.142857	0.724659	7.708647
Within	56	4	14
Total	116	7

In the context of your problem:

ANOVA
Source of Variation	Sum of Square	Degrees of Freedom	Mean Square	F	P-value	F crit
Factor 1	8	1	8	0.571429	0.491767	7.708647
Factor 2	50	1	50	3.571429	0.131778	7.708647
Interaction	2	1	2	0.142857	0.724659	7.708647
Error	56	4	14
Total	116	7