Music Preferences Reflective and Upbeat Energetic Intense Totals personalit Comp
ID: 3222918 • Letter: M
Question
Music Preferences Reflective and Upbeat Energetic Intense Totals personalit Complex and and and Conventio Rhythmic Rebelliou nal 44 30 100 Introvert 20 Extrovert 180 34 50 36 300 Totals 200 40 80 80 400 Suitable null and alternative hypotheses might be: Ho: Music preference is not associated with personality, and H1: Music preference is associated with personality 1. Plot the data presented in the contingency table. (10%) 2. What is the best way to calculate the correlation between these two variables? And why? (10%) 3. Calculate the correlation between these two variables and interpret the result. (20%)Explanation / Answer
a)
Personality
Reflective & Complex
Upbeat & Conventional
Energetic & Rhythmic
Intense & Rebellious
Totals
Introvert
20 (50)
6 (10)
30 (20)
44 (20)
100
Extrovert
180 (150)
34 (30)
50 (60)
36 (60)
300
Totals
200
40
80
80
400
Factors
0.5
0.1
0.2
0.2
b)
Best way would be to calculate would be through chi-square test.
c)
Personality
Reflective & Complex
Upbeat & Conventional
Energetic & Rhythmic
Intense & Rebellious
Totals
Introvert
20 (50)
6 (10)
30 (20)
44 (20)
100
Extrovert
180 (150)
34 (30)
50 (60)
36 (60)
300
Totals
200
40
80
80
400
Factors
0.5
0.1
0.2
0.2
Factors calculated as (20+180)/(100+300)=0.5, (6+34)/(100+300)=0.1, (30+20)/(100+300)=0.2, (44+36)/(100+300)=0.2
x^2STAT=E(f0-fe)^2/fe
=(20-50)^2/50+(6-10)^2/10+……..(36-60)^2/60
=18+1.6+5+28.8+6+0.533333+1.666667+9.6
=71.2
a at 0.05 with three DF is 7.8147. 71.2 is greater than 7.8147. Hence, reject the null hypothesis.
Personality
Reflective & Complex
Upbeat & Conventional
Energetic & Rhythmic
Intense & Rebellious
Totals
Introvert
20 (50)
6 (10)
30 (20)
44 (20)
100
Extrovert
180 (150)
34 (30)
50 (60)
36 (60)
300
Totals
200
40
80
80
400
Factors
0.5
0.1
0.2
0.2
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