Question

As researcher you wonder if can teach old cats new tricks, so you adopted 10 kittens and 10 old cats. You attempt to teach the cats 2 tricks: sitting and rolling over and you record how many days it would take for each to learn the trick.
(Note: this is a 2x2 factorial analysis of variance)
The four populations are as follows:
Population 1: Old cats who are to learn sitting.
Population 2: Old cats who are to learn rolling over.
Population 3: Kittens who are to learn sitting.
Population 4: Kittens who are to learn rolling over.

What are the three null hypotheses and three alternative hypotheses?

Answer 1

Objective: To study the effect of 2 factors - Age of the cat (2 levels - Old cats and kittens) and the type of trick it is made to perform (2 levels - Sitting and Rolling over) and the interaction effect, if present on the number of days taken to

Here, the dependent variable is the number of days taken to learn the trick and the factors studies are Age and Type of Trick. We would attain the objective mentioned above by running the appropriate statistical test - Two way ANOVA to test the following hypothesis:

H₀₁: Age has no effect on time taken to lean a new trick H₀₂: The type of trick has no effect on time taken to learn it. H₀₃: There is no interaction effect (interaction between Age and Type of trick) on the time taken to learn the trick.

Vs

H_a1: Age significantly affects the time taken to lean a new trick H_a2: The type of trick significantly affects the time taken to learn it.        H_a3: There is a significant interaction effect (interaction between Age and Type of trick) on the time taken to learn the trick.

If denote the essect of Age and Type of trick on time taken to learn it.

   Vs