- Sharma believes that each computer game he sells appeals equally to all age ranges.
To investigate this, he takes a random sample of 100 people who play these games and asks them which of the games \(A , B\) or \(C\) they prefer.
The results are summarised in the table below.
| Computer game | \(A\) | \(B\) | \(C\) |
| \multirow{3}{*}{Age range} | \(< 20\) | 8 | 15 | 6 |
| \cline { 2 - 5 } | \(20 - 30\) | 21 | 12 | 9 |
| \cline { 2 - 5 } | \(> 30\) | 6 | 10 | 13 |
- Write down hypotheses for a suitable test to assess Sharma's belief.
- For the test, calculate the expected frequency for
- those players aged under 20 who prefer game \(C\)
- those players aged between 20 and 30 who prefer game \(A\)
- State the degrees of freedom of the test statistic for this test.
Sharma correctly calculates the test statistic for this test to be 11.542 (to 3 decimal places).
- Using a \(5 \%\) significance level, and stating your critical value, comment on Sharma's belief.