Compute an ANOVA with statistical software (or manually), and use the .05 signif

Question

Compute an ANOVA with statistical software (or manually), and use the .05 significance level to answer the following questions.

a. Is there a difference in the Size means?

b. Is there a difference in the Weight means?

c. Is there a significant interaction between Weight and Size?

Size

                                Small     Medium               Large

Weight Heavy   23           20           11

21           32           20

25           26           20

Light      13           20           11

32           17           23

17           15          

8

Explanation / Answer

We will use minitab software to Answer this question.

The ANOVA table for this question is

Source DF SS MS F P
weight 1 98.000 98.0000 2.48 0.141
size 2 156.333 78.1667 1.98 0.180
Interaction 2 36.333 18.1667 0.46 0.642
Error 12 473.333 39.4444
Total 17 764.000

Here we will make decision about question a,b and c through the p-value given in the table

a) The p-value for difference in the Size is 0.141 >0.05 then we are fail to rehect Hypothesis that all sizes are equal. Hence we claim that all effect of size are same.

b) The p-value for difference in the Weight is  0.180 >0.05 then we are fail to rehect Hypothesis that all weights are equal. Hence we claim that all effect of weight are same.

c) The p-value for significant interaction between Weight and Size is 0.642>0.05 then we are fail to rehect Hypothesis that there is no interaction between sizes and weights. Hence we claim that all effect of nteraction between sizes and weights is zero.

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