Standard +0.3 This is a straightforward one-sample t-test with small sample size. Students must calculate sample mean and standard deviation from 6 values, set up hypotheses correctly (one-tailed test), find the t-statistic, and compare to critical value. While it requires multiple steps and careful calculation, it follows a standard procedure taught explicitly in S3 with no conceptual surprises or novel problem-solving required. Slightly above average difficulty due to calculation demands and potential for arithmetic errors.
2 A coffee machine used in a bar is claimed by the manager to dispense 170 ml of coffee per cup on average. A customer believes that the average amount of coffee dispensed is less than 170 ml . She measures the amount of coffee in 6 randomly chosen cups. The results, in ml , are as follows.
$$\begin{array} { l l l l l l }
167 & 171 & 164 & 169 & 168 & 166
\end{array}$$
Assuming a relevant normal distribution, test the manager's claim at the 5\% significance level.
2 A coffee machine used in a bar is claimed by the manager to dispense 170 ml of coffee per cup on average. A customer believes that the average amount of coffee dispensed is less than 170 ml . She measures the amount of coffee in 6 randomly chosen cups. The results, in ml , are as follows.
$$\begin{array} { l l l l l l }
167 & 171 & 164 & 169 & 168 & 166
\end{array}$$
Assuming a relevant normal distribution, test the manager's claim at the 5\% significance level.
\hfill \mbox{\textit{OCR S3 2010 Q2 [7]}}