4 A survey of a random sample of 250 people is carried out. Their musical preferences are categorized as pop, classical or jazz. Their ages are categorized as under 25, 25 to 50, or over 50. The results are as follows.
| \multirow{2}{*}{} | Musical preference | \multirow{2}{*}{Row totals} |
| | Pop | Classical | Jazz | |
| \multirow{3}{*}{Age group} | Under 25 | 57 | 15 | 12 | 84 |
| 25-50 | 43 | 21 | 21 | 85 |
| Over 50 | 22 | 32 | 27 | 81 |
| Column totals | 122 | 68 | 60 | 250 |
- Carry out a test at the \(5 \%\) significance level to examine whether there is any association between musical preference and age group. State carefully your null and alternative hypotheses. Your working should include a table showing the contributions of each cell to the test statistic.
- Discuss briefly how musical preferences vary between the age groups, as shown by the contributions to the test statistic.