Question

A survey result of radio listeners preference for different type of music under various work group as follow
Types of musical preference 18-25 26-35 above 36
National 80 60 9
Foreign 210 325 44
Indifference 16 45 132
Is preference for type of music influence by age? Test and comment
Table value=9.488

Answer 1

Observed values

Types 18-25 26-35 above 36 Total

National 80 60 9 149

Foreign 210 325 44 579

Indifference 16 45 132 193

Total 306 430 185 921

Expected values: $e_{ij}=\frac{T_iT_j}{T}$

Expected values

Types 18-25 26-35 above 36

National 49.50 69.57 29.93

Foreign 192.37 270.33 116.30

Indifference 64.12 90.11 38.77

Null hypothesis: the preference for type of music does not influenced by age

Alternative hypothesis: the preference for type of music influenced by age

Test statistic: $\chi^2=\Sigma_{i=1}^3\Sigma_{j=1}^3\frac{(o_{ij}-e_{ij})^2}{e_{ij}}=375.27$

Degrees of freedom: $df=(r-1)(c-1)=(3-1)(3-1)=4.$

Since the test statistic is greater than the critical value (9.488), reject the null hypothesis.

The preference for type of music influenced by age.