H2 Maths 2012 A Level Solution Paper 2 Q6; H2 Maths Group Tuition

6(i)

$H_0: \mu=14.0 cm$

$H_1: \mu\neq 14.0 cm$

(ii)

$\bar{x}\sim N(14,\frac{3.8^2}{20})$

For the null hypothesis not to be rejected,

$Z_{2.5\%}<\frac{\bar{x}-14}{3.8/\sqrt{20}}<Z_{97.5\%}$

$-1.95996<\frac{\bar{x}-14}{3.8/\sqrt{20}}<1.95996$ (use GC invNorm function!)

$12.3<\bar{x}<15.7$ (3 s.f.)

(iii) Since $\bar{x}=15.8$ is out of the set $12.3<\bar{x}<15.7$ , the null hypothesis would be rejected. There is sufficient evidence that the squirrels on the island do not have the same mean tail length as the species known to her.

(technique: put in words what $H_1$ says!)

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