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(i)

Let X denotes the length of a leaf in cm.

Under approximately by Central Limit Theorem since n is large.

From Graphing Calculator, p-value .

Thus we reject , and conclude with sufficient evidence at 5% level of significant that the mean length of the leaf is less than 7 cm.

(ii)

Unbiased estimate of

Unbiased estimate of

(iii)

Under approximately by Central Limit Theorem since n is large.

From Graphing Calculator, p-value .

Since is rejected, p-values

Required set of values $latex = \{ \alpha \in \mathbb{R}: 1.97 \le \alpha \le 100 \}

### KS Comments

Nothing special about this question. Students still forget to introduce Central Limit Theorem when doing the hypothesis testing though. Lastly, the question asks for the set of values, so students should use precise set notation.