The calculation for a factorial experiment involving FOUR LEVELS of factor A, TH

Question

The calculation for a factorial experiment involving FOUR LEVELS of factor A, THREE LEVELS OF Factor B, and THREE REPLICATIONS resulted in the following data: SST= 280, SSA= 26, SSAB=175. Setup the ANOVA table and test for any significant main effects and any intersection effect. use a=0.05.

A1. State the null and alternative hypothesis?

A2. What is the value of the test statistic?

A3. What is the critical value?

A4. What is the p-value?

A5. What is your conclusion regarding the null hypothesis?

Explanation / Answer

A1. The null and alternative hypothesis is

H0 : The population means of all groups under consideration are equal.

H1: The means are not all equal.

H0: There is no interaction between the factors.
H1: There is an interaction between the factors.

A2. The value of the test statistic is

SST=280, SSA=26, SSAB=175, SSB=280-26-175=79

A3. The critical value is

For factor A, tabulated value of F is 4.76

For factor B, tabulated value of F is 5.14

A5. Reject Ho when F> F-tabulated

Here Both is less than F-tabulated so, we donot reject H0

Source SS df MS F-statistic Factor A 26 3 8.666667 0.297143 Factor B 79 2 39.5 1.354286 Error 175 6 29.16667 Total 280 11

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