2014 A-level H1 Mathematics (8864) Question 10 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Let X denotes the length of a leaf in cm.

H_0: \mu = 7

H_0: \mu < 7

Under H_0, \bar{X} ~\sim~ N(7, \frac{4.4}{50}) approximately by Central Limit Theorem since n is large.

From Graphing Calculator, p-value = 0.0459 < 0.05.

Thus we reject H_0, 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 \mu = \frac{310.4}{50} = 6.208

Unbiased estimate of {\sigma}^{2} = \frac{1}{49}[2209.2 - \frac{310.4^{2}}{50}] = 5.76

(iii)

H_0: \mu = 7

H_0: \mu \ne 7

Under H_0, \bar{X} ~\sim~ N(7, \frac{5.79935}{50}) approximately by Central Limit Theorem since n is large.

From Graphing Calculator, p-value = 0.019624.

Since H_0 is rejected, p-values \le \alpha \%

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.

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