A farmer grows large amounts of a certain crop. On average, the yield per plant has been 0.75 kg . The farmer has improved the soil in which the crop grows, and she claims that the yield per plant has increased. A random sample of 10 plants grown in the improved soil is chosen. The yields, \(x \mathrm{~kg}\), are summarised as follows.
\[\Sigma x=7.85 \quad \Sigma x^{2}=6.19\]
(i) Test at the 5\% significance level whether the farmer's claim is justified, assuming a normal distribution.
(ii) Find a 95\% confidence interval for the population mean yield for plants grown in the new soil.