CAIE A-Level Further Math A2 4.2.1 Hypothesis Tests Questions

Practise setting up and interpreting hypothesis tests for population claims using Further Mathematics AS questions and mark schemes.

Exam points

Apply hypothesis tests to assess claims about population parameters using sample evidence.

[Maximum number: 7]

A large number of children are competing in a throwing competition. The distances, in metres, thrown by a random sample of 8 children are as follows.
19.8
20.8
21.5
22.1
23.7
24.4
25.0
26.3

Assuming that distances are normally distributed, test, at the 5% significance level, whether the population mean distance thrown is more than 22.0 metres.

$\sum x=183.6, \sum x^{2}=4249.08, \bar{x}=22.95$ $s^{2}=\frac{1}{7}\left(4249.08-\frac{183.6^{2}}{8}\right)=5.066$ $\mathrm{H}_{0}: \mu=22.0, \quad \mathrm{H}_{1}: \mu>22.0$ $t=\frac{22.95-22.0}{\sqrt{\frac{s^{2}}{8}}}=1.194$
Compare t with correct tabular value 1.895
Accept $\mathrm{H}_{0}$ : mean distance thrown is not more than 22.0 m
5a 7

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CAIE A-Level Further Math A2 4.2.1 Hypothesis Tests Questions question 1