Compute an ANOVA with statistical software or manually and u

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

Solution

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.