Standard +0.3 This is a straightforward one-sample t-test with clear hypotheses (μ < 568), small sample size requiring t-distribution, and standard procedure. While it requires multiple steps (calculate sample mean/SD, find t-statistic, compare to critical value), each step is routine for S2 level. The 10 marks reflect length rather than conceptual difficulty—slightly above average only because students must recognize to use t-test (variance unknown) and correctly interpret one-tailed test at 1% level.
6 The contents, in millilitres, of cartons of milk produced at Kream Dairies, can be modelled by a normal distribution with mean 568 and variance \(\sigma ^ { 2 }\).
After receiving several complaints from their customers who thought that the average content of the cartons had been reduced, the production manager of Kream Dairies decided to investigate.
A random sample of 8 cartons of milk was taken, revealing the following contents, in millilitres.
$$\begin{array} { l l l l l l l l }
560 & 568 & 561 & 562 & 564 & 567 & 565 & 563
\end{array}$$
Investigate, at the \(1 \%\) level of significance, whether the average content of cartons of milk is less than 568 millilitres.
(10 marks)
6 The contents, in millilitres, of cartons of milk produced at Kream Dairies, can be modelled by a normal distribution with mean 568 and variance $\sigma ^ { 2 }$.
After receiving several complaints from their customers who thought that the average content of the cartons had been reduced, the production manager of Kream Dairies decided to investigate.
A random sample of 8 cartons of milk was taken, revealing the following contents, in millilitres.
$$\begin{array} { l l l l l l l l }
560 & 568 & 561 & 562 & 564 & 567 & 565 & 563
\end{array}$$
Investigate, at the $1 \%$ level of significance, whether the average content of cartons of milk is less than 568 millilitres.\\
(10 marks)
\hfill \mbox{\textit{AQA S2 2005 Q6 [10]}}