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 a =.05. Factor A is method of loading and unloading; Factor B is the type of ride. Type of Ride Roller Coaster Screaming Demon Method 1 45 Method 2 49 Set up the ANOVA table (to whole number, but p-value to 2 dedmals and value to 1 decimal, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Factor A Factor B Interaction

Answer 1

Answer Date: 11/11/2019 To test the hypothesis is that there is a significant effect due to loading and unloading method at 5% level of significance. The null and alternative hypothesis is, H:/4 = 12 H,: at least one p, is unequal. To test the hypothesis is that there is a significant effect due to type of ride at 5% level of significance. The null and alternative hypothesis is, H :14 = 12 = 11 H : at least one uis unequal. To test the hypothesis is that there is an interaction effect between method and type of ride at 5% level of significance. The null and alternative hypothesis is,

The null hypothesis is that there is no interaction effect between method and type of ride. The alternative hypothesis is that there is an interaction effect between method and type of ride. The F-test statistics for methods is, By using Excel software, find F-test statistics with the help of following steps: 1) Import the data. 2) Choose ANOVA: Two Factor With Replication from Data Analysis in Data menu. Choose Input Range. 4) Choose Output Range. 5) Click Ok. 3) SS df MS F 1 ANOVA Source of Variation Method (Factor A) Type of ride (Factor B) Interaction Within Total 1.3 24 1.3 12 25.3 10 0.1 1.2 2.5 P-value Fcrit 0.73 5.987377584 0.36 5.14325285 0.16 5.14325285 50.7 60 136 6 11

From the Excel output, the F-test statistics for methods is 0.1. The p-value for this test is, From the Excel output, the p value for this test is 0.73|. The F-test statistics for type of ride is, From the Excel output, the F-test statistics for type of ride is (1.2). The p-value for this test is, From the Excel output, the p value for this test is 0.36. The F-test statistics for interaction is, From the Excel output, the F-test statistics for interaction is 2.5. The p-value for this test is, From the Excel output, the p value for this test is 0.16.

Decision The conclusion is that p-value in this context is higher than 0.05 which is 0.73, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a significant effect due to loading and unloading method. The result is not statistically significant. The conclusion is that p-value in this context is higher than 0.05 which is 0.36, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is a significant effect due to type of ride. The result is not statistically significant. The conclusion is that p-value in this context is higher than 0.05 which is 0.16, so the null hypothesis is not rejected at 5% level of significance. There is insufficient evidence to indicate that there is an interaction effect between method and type of ride. The result is not statistically significant.