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A market researcher is interested in determining whether the age of listeners influences their preferred musical...

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Basic Math

A market researcher is interested in determining whether the ageof listeners influences their preferred musical styles. Thefollowing is a contingency table from a random sample of 385individuals:

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 variablesindependent?

Answer & Explanation Solved by verified expert
4.3 Ratings (928 Votes)

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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