7. A student collects data on whether competitors in local tennis tournaments are right, or left-handed. The table below shows the number of left-handed players who reached the last 16 for fifty tournaments.
| No. of Left-handed Players | 0 | 1 | 2 | 3 | 4 | \(\geq 5\) |
| No. of Tournaments | 4 | 12 | 18 | 11 | 5 | 0 |
The student believes that a binomial distribution with \(n = 16\) and \(p = 0.1\) could be a suitable model for these data.
- Stating your hypotheses clearly test the student's model at the \(5 \%\) level of significance.
(13 marks)
To improve the model the student decides to estimate \(p\) using the data in the table. Using this value of \(p\) to calculate expected frequencies the student had 5 classes after combining and calculated that \(\sum \frac { ( O - E ) ^ { 2 } } { E } = 2.127\) - Test at the \(5 \%\) level of significance whether or not the binomial distribution is a suitable model for the number of left-handed players who reach the last 16 in local tennis tournaments.
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