7 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.