Standard +0.3 This is a straightforward one-sample t-test application with clear hypotheses (μ < 11.8), small sample requiring calculation of sample mean and standard deviation, and standard critical value comparison. While it requires proper test structure and calculation accuracy, it follows a standard template with no conceptual surprises, making it slightly easier than average for S3 level.
3 An athlete finds that her times for running 100 m are normally distributed. Before a period of intensive training, her mean time is 11.8 s . After the period of intensive training, five randomly selected times, in seconds, are as follows.
$$\begin{array} { l l l l l }
11.70 & 11.65 & 11.80 & 11.75 & 11.60
\end{array}$$
Carry out a suitable test, at the \(5 \%\) significance level, to investigate whether times after the training are less, on average, than times before the training.
3 An athlete finds that her times for running 100 m are normally distributed. Before a period of intensive training, her mean time is 11.8 s . After the period of intensive training, five randomly selected times, in seconds, are as follows.
$$\begin{array} { l l l l l }
11.70 & 11.65 & 11.80 & 11.75 & 11.60
\end{array}$$
Carry out a suitable test, at the $5 \%$ significance level, to investigate whether times after the training are less, on average, than times before the training.
\hfill \mbox{\textit{OCR S3 2014 Q3 [7]}}