1 A machine fills bottles with bleach. The volume, in millilitres, of bleach dispensed by the machine into a bottle may be modelled by a normal distribution with mean \(\mu\) and standard deviation 8 . A recent inspection indicated that the value of \(\mu\) was 768 . Yvonne, the machine's operator, claims that this value has not subsequently changed. Zara, the quality control supervisor, records the volume of bleach in each of a random sample of 18 bottles filled by the machine and calculates their mean to be 764.8 ml . Test, at the \(5 \%\) level of significance, Yvonne's claim that the mean volume of bleach dispensed by the machine has not changed from 768 ml .

# Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $H_0: \mu = 768$ and $H_1: \mu \neq 768$ | B1 | Both required |
| Test statistic: $z = \dfrac{764.8 - 768}{\dfrac{8}{\sqrt{18}}}$ | M1 | |
| $= -1.70$ | A1 | $(-1.697)$ |
| $z_{crit} = \pm 1.96$ | B1 | $z_{crit} = 1.96$ or $z_{crit} = -1.96$ |
| $\Rightarrow$ Accept $H_0$ | A1 | |
| No evidence at the 5% level of significance to deny Yvonne's claim | E1 | |
| **Total** | **6** | |

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1 A machine fills bottles with bleach. The volume, in millilitres, of bleach dispensed by the machine into a bottle may be modelled by a normal distribution with mean $\mu$ and standard deviation 8 .

A recent inspection indicated that the value of $\mu$ was 768 . Yvonne, the machine's operator, claims that this value has not subsequently changed.

Zara, the quality control supervisor, records the volume of bleach in each of a random sample of 18 bottles filled by the machine and calculates their mean to be 764.8 ml .

Test, at the $5 \%$ level of significance, Yvonne's claim that the mean volume of bleach dispensed by the machine has not changed from 768 ml .

\hfill \mbox{\textit{AQA S2 2009 Q1 [6]}}