7. A teacher thinks that \(20 \%\) of the pupils in a school read the Deano comic regularly.
He chooses 20 pupils at random and finds 9 of them read the Deano.
- Test, at the \(5 \%\) level of significance, whether or not there is evidence that the percentage of pupils that read the Deano is different from 20\%. State your hypotheses clearly.
- State all the possible numbers of pupils that read the Deano from a sample of size 20 that will make the test in part (a)(i) significant at the \(5 \%\) level.
(9)
The teacher takes another 4 random samples of size 20 and they contain 1, 3, 1 and 4 pupils that read the Deano.
- By combining all 5 samples and using a suitable approximation test, at the \(5 \%\) level of significance, whether or not this provides evidence that the percentage of pupils in the school that read the Deano is different from 20\%.
- Comment on your results for the tests in part (a) and part (b).