1 At the start of the 2012 season, the ages of the members of the Warwickshire Acorns Cricket Club could be modelled by a normal random variable, \(X\) years, with mean \(\mu\) and standard deviation \(\sigma\). The ages, \(x\) years, of a random sample of 15 such members are summarised below. $$\sum x = 546 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 1407.6$$

1. Construct a \(98 \%\) confidence interval for \(\mu\), giving the limits to one decimal place.
   (6 marks)
2. At the start of the 2005 season, the mean age of the members was 40.0 years. Use your confidence interval constructed in part (a) to indicate, with a reason, whether the mean age had changed.