A greengrocer is investigating the weights of two types of orange, type $$\(A\)$$ and type $$\(B\)$$. She believes that on average type $$\(A\)$$ oranges weigh greater than 5 grams more than type $$\(B\)$$ oranges. She collects a random sample of 40 type $$\(A\)$$ oranges and 32 type $$\(B\)$$ oranges and records the weight, $$\(x\)$$ grams, of each orange. The table shows a summary of her data. Explain how you have used the fact that the sample sizes are large in your answer to part (b). (2)

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