1. Past evidence shows that \(7 \%\) of pears grown by a farmer are unfit for sale.

This season it is believed that the proportion of pears that are unfit for sale has decreased. To test this belief a random sample of \(n\) pears is taken. The random variable \(Y\) represents the number of pears in the sample that are unfit for sale.

1. Find the smallest value of \(n\) such that \(Y = 0\) lies in the critical region for this test at a \(5 \%\) level of significance. In the past, \(8 \%\) of the pears grown by the farmer weigh more than 180 g . This season the farmer believes the proportion of pears weighing more than 180 g has changed. She takes a random sample of 75 pears and finds that 11 of them weigh more than 180 g .
2. Test, using a suitable approximation, whether there is evidence of a change in the proportion of pears weighing more than 180 g .
   You should use a \(5 \%\) level of significance and state your hypotheses clearly.