dieting depend on exercise. They give four groups (N- 20 per group) a and measur

Question

dieting depend on exercise. They give four groups (N- 20 per group) a and measure weight loss in pounds after three months di the eest whether diet and esercise impact weight loss. They are very intere M-2, SD Column Means Drovi factorial ANOoVA on this data, using the information from the ANOV A table the main pelow (you will need to fill in some information). Test the main effect of exercise, Carry o h effect of diet, and the interaction effect. Assume a-.o5 ate question as a research hypothesis and a null hypothesis about populations. Diet Main Effect: hypothesis (H):euc on impa ct onDiet. ail be no impact on Dict. Null hypothesis (Ho): There uait Exercise Main Effeet: esearch hypothesis (H): There r4ill be an ì mpact on exercise Null hypothesis (Ho): There wil?no impact on exercise. nteraction Effecet: Dictmain cffect X exeraise main cfect esearch hypothesis (Hi): There will be an intcraction btwn Dictandcxerc Null hypothesis (Ho): Thac rill be no intcraction utin dict andcxcertuse

Explanation / Answer

We have given that row means and column means. We have to do factorial anova on this data.

Degrees of freedoms :

Dfcolumns = 2-1 = 1

Dfrows = 2-1 = 1

Dfinteraction = 4-1-1-1 = 1

Dfwithin = 20-4 = 16

Dftotal = 20-1 = 19

Also we have given that,

Critical value for F-distribution is = 4.49

MScolumns = SScolumns / dfcolumns = 20.55/1 = 20.55

MSrows = SSrows / dfrows = 17.63/1 = 17.63

MSinteraction = 38.18 / 1 = 38.18

MSwithin = 459.39 / 16 = 28.71

Now we have to find F-rstios.

Fcolumns = MScolumns / MSwithin = 20.55 / 28.71 = 0.72

Frows = MSrows / MSwithin = 17.63 / 28.71 = 0.61

Finteraction = MSinteraction / MSwithin = 38.18 / 28.71 = 1.33

Now we can see that,

F-statistic for columns , rows and interaction is less than critical value.

Accept H0 at 5% level of significance.

Conclusion : There will be no impact on diet.

There will be no impact on exercise.

There will be no interaction between diet and exercise.

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