6. A greengrocer sells apples from a barrel in his shop. He claims that no more than \(5 \%\) of the apples are of poor quality. When he takes 10 apples out for a customer, 2 of them are bad.

1. Stating your hypotheses clearly, test his claim at the \(1 \%\) significance level.
2. State an assumption that has been made about the selection of the apples.
3. When five other customers also buy 10 apples each, the numbers of bad apples they get are \(1,3,1,2\) and 1 respectively. By combining all six customers' results, and using a suitable approximation, test at the \(1 \%\) significance level whether the combined results provide evidence that the proportion of bad apples in the barrel is greater than \(5 \%\).
4. Comment briefly on your results in parts (a) and (c).