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 α-.05. Factor A is method of loading and unloading; Factor B is the type of ride. Type of Ride Roller Coaster 47 49 52 54 Screaming Demon 54 46 Long Flume 53 49 49 45 Method 1 Method 2 51 a. Set up the ANOVA table (to 2 decimal, if necessary) Round p-value to four decimal places. Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Factor A Factor B Interaction Error 10.000 Total

Answer 1

We can use excel to perform 2 way ANOVA with replication .

Go to Data menu ---> Data analysis ---> Anova: Two-Factor With Replication.

日勺. calculations Excel (Product Activation Failed) Data Analysis Analysis Tools View Tell me what you wa Home InsertPage Layout Formulas File @connections 虬 E Properties +Data Analysis Clear show Queries 困 Anova: Single Factor Anova: Two Factor With Replication EEE From Table Get ExternalNew Cancel Refresh Text to Recent Sources Columns cod | Anova: Two- correlation Factor without Replication Replication QueryRecent Sources Get &Transform Advanced ubtotal All-QEdit Links Sort Filter Reapply Help Covariance Descriptive StatisticS Exponential Smoothing F-Test Two-Sample tor Variances Fourier Analysis Histogram Sort & Filter Analysis utline F3 0

Then plug the Inputs as shown below :

For Input range : Select the entire data set

Rows per sample : 2

Then click on OK tab.

Roller coaster Screaming Demon Long Flume Anova: Two-Factor With Replication 2 Method 1 47 49 52 54 53 49 49 54 IInput OK Cancel Help SAS1:SDS5 nput Range: 4 Method 2 Rows per sample: 51 Alpha: 0.05 Output options O Qutput Range ONew Worksheet Ply: O New Workbook 12

The ANOVA table is as follows

ANOVA Source of Variation Sample Column:s Interaction Within df p-value SS 5.333333 12.66667 44.66667 Ms F crit 1 5.333333 0.533333 0.492726 5.987377607 2 6.333333 0.633333 0.562922 5.14325285 2 22.33333 2.233333 0.188377 5.14325285 10 60 Total 122.6667

We are asked to round the values to 2 decimal places and p value for 4 decimals :

MS 5.33 6.33 22.33 10 p value 0.4927 df Factor A Factor B Interaction Error Total 5.33 12.67 44.67 60 122.67 0.53 0.63 2.23