Question
In: Math
A market researcher is interested in determining whether the age of listeners influences their preferred musical...
A market researcher is interested in determining whether the age of listeners influences their preferred musical styles. The following is a contingency table from a random sample of 385 individuals:
AGE
Style_1
Style_2
Style_3
18–25
125
13
6
26–35
87
12
6
36–45
50
22
12
46+
12
25
15
A) what are the numerator degrees of freedom
B) what are the denominator degrees of freedom.
C) Calculate the value of the test statistic – Chi-Square.
D) Using the 95% level of confidence, are these two variables independent?
Solutions
Expert Solution
| c1 | c2 | c3 | c4 | sum | |||||||||
| r1 | 125 | 87 | 50 | 12 | 274 | ||||||||
| r2 | 13 | 12 | 22 | 25 | 72 | ||||||||
| r3 | 6 | 6 | 12 | 15 | 39 | ||||||||
| sum | 144 | 105 | 84 | 52 | 385 | ||||||||
| Eij | 1 | 2 | 3 | 4 | |||||||||
| expected | 1 | 102.4831169 | 74.72727 | 59.78182 | 37.00779 | ||||||||
| 2 | 26.92987013 | 19.63636 | 15.70909 | 9.724675 | |||||||||
| 3 | 14.58701299 | 10.63636 | 8.509091 | 5.267532 | |||||||||
| 0i | 125 | 87 | 50 | 12 | 13 | 12 | 22 | 25 | 6 | 6 | 12 | 15 | |
| Ei | 102.4831169 | 74.72727 | 59.78182 | 37.00779 | 26.92987 | 19.63636 | 15.70909 | 9.724675 | 14.58701 | 10.63636 | 8.509091 | 5.267532 | |
| (Oi-Ei)^2/Ei | 4.94725415 | 2.015594 | 1.600553 | 16.89886 | 7.20543 | 2.969697 | 2.519276 | 23.99417 | 5.054962 | 2.020979 | 1.432168 | 17.98203 | |
| sum | 88.64097952 | ||||||||||||
| critical value | 12.59158724 | ||||||||||||
| p-value | 5.80265E-17 | ||||||||||||
a)
numerator df = 3-1 = 2
b)
denominator df = 4-1 = 3
c)
TS = 88.64
d)
p-value = 0.0000 < 0.05
hence we reject the null hypothesis , two variables are dependent
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