9231 P21 - Jun 2017 - Q7 - 7 marks
6146
A farmer grows a particular type of fruit tree. On average, the mass of fruit produced per tree has been 6.2 kg . He has developed a new kind of soil and claims that the mean mass of fruit produced per tree when growing in this new soil has increased. A random sample of 10 trees grown in the new soil is chosen. The masses, \(x \mathrm{~kg}\), of fruit produced are summarised as follows.
\[\Sigma x=72.0 \quad \Sigma x^{2}=542.0\]
Test at the 5\% significance level whether the farmer's claim is justified, assuming a normal distribution.
