Past evidence shows that $$\(7 \%\)$$ of pears grown by a farmer are unfit for sale. This season it is believed that the proportion of pears that are unfit for sale has decreased. To test this belief a random sample of $$\(n\)$$ pears is taken. The random variable $$\(Y\)$$ represents the number of pears in the sample that are unfit for sale. (a) Find the smallest value of $$\(n\)$$ such that $$\(Y=0\)$$ lies in the critical region for this test at a $$\(5 \%\)$$ level of significance. (3) In the past, $$\(8 \%\)$$ of the pears grown by the farmer weigh more than $$\(180 \mathrm{~g}\)$$. This season the farmer believes the proportion of pears weighing more than $$\(180 \mathrm{~g}\)$$ has changed. She takes a random sample of 75 pears and finds that 11 of them weigh more than $$\(180 \mathrm{~g}\)$$. (b) Test, using a suitable approximation, whether there is evidence of a change in the proportion of pears weighing more than $$\(180 \mathrm{~g}\)$$. You should use a 5\% level of significance and state your hypotheses clearly. (6)

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