Statistics Solutions

[Solution] A psychologist would like to learn about the effect of anxiety over the capacity that people possess to learn new materials. This investigation

Question: A psychologist would like to learn about the effect of anxiety over the capacity that people possess to learn new materials. This investigation also pretends to learn if the effect of the anxiety depends on the difficulty of the new material. For that, they make an experiment with three different levels of anxiety (high, medium, low) and three levels of difficulty ( high, medium, low). After selecting randomly the data of the sample, the results are the following:

Anxiety
Difficulty of material Low Medium High
Low 18
20
17
17
16 		18
19
17
18
15 		18
16
19
17
18
Medium 18
20
17
17
16 		18
18
14
17
15 		14
17
16
15
12
High 11
10
8
6
10 		15
13
12
12
11 		9
7
5
8
8

Make an ANOVA in two directions with a level of significance of 0.05 and answer:

Is the variable "difficulty of material" meaningful for the learning of new material?

Is the variable "anxiety" meaningful for the learning of new material?

Is the interaction "anxiety – difficulty of material" meaningful for the learning of new material?

Which one is the null hypothesis and the alternative for the ANOVA of two directions like this?

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