Further Math ASs 4.2.1 Hypothesis tests

[Maximum number: 6]

Maya is an athlete who competes in 1500 -metre races. Last summer her practice run times had mean 4.22 minutes. Over the winter she has done some intense training to try to improve her times. A random sample of 10 of her practice run times, x minutes, this summer are summarised as follows.

\sum x=42.05 \quad \sum x^{2}=176.83

Maya's new practice run times are normally distributed. She believes that on average her times have improved as a result of her training.

Test, at the 5% significance level, whether Maya's belief is supported by the data.

$\mathrm{H}_{0}: \mu=4.22 \quad \mathrm{H}_{1}: \mu<4.22$ $\bar{x}=\frac{42.05}{10}[=4.205], \quad s^{2}=\frac{1}{9}\left(176.83-\frac{42.05^{2}}{10}\right)\left[=\frac{13}{12000}=0.0010833\right]$ $t=\frac{4.205-4.22}{\sqrt{\frac{s^{2}}{10}}}$
Their 4.205, their $s^{2}$ .

t=-1.44
Condone sign.

Tabular value =1.833: ' 1.44 ' <1.833, accept $\mathrm{H}_{0}$
Compare their value with correct tabular value, signs
consistent, allow 'not significant'.

There is insufficient evidence to support Maya's belief.
Correct conclusion in context, following correct work,
level of uncertainty in language.
A0 if hypotheses wrong way round or missing.

6

CAIE A-Level Further Math AS 4.2.1 Hypothesis Tests Questions

Exam points

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