Standard +0.3 This is a straightforward two-tailed hypothesis test with clearly stated hypotheses, given summary statistics, and standard procedure. Students must calculate the sample mean (83.5), use the normal distribution with known variance, compute a z-statistic, and compare to critical values. While it requires multiple steps, each is routine for S2 level with no conceptual challenges or novel problem-solving required—slightly easier than average due to its mechanical nature.
3 The handicap committee of a golf club has indicated that the mean score achieved by the club's members in the past was 85.9 .
A group of members believes that recent changes to the golf course have led to a change in the mean score achieved by the club's members and decides to investigate this belief.
A random sample of the scores, \(x\), of 100 club members was taken and is summarised by
$$\sum x = 8350 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 15321$$
where \(\bar { x }\) denotes the sample mean.
Test, at the \(5 \%\) level of significance, the group's belief that the mean score of 85.9 has changed.
3 The handicap committee of a golf club has indicated that the mean score achieved by the club's members in the past was 85.9 .
A group of members believes that recent changes to the golf course have led to a change in the mean score achieved by the club's members and decides to investigate this belief.
A random sample of the scores, $x$, of 100 club members was taken and is summarised by
$$\sum x = 8350 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 15321$$
where $\bar { x }$ denotes the sample mean.\\
Test, at the $5 \%$ level of significance, the group's belief that the mean score of 85.9 has changed.
\hfill \mbox{\textit{AQA S2 2007 Q3 [8]}}