9 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.
$$\Sigma x = 7.85 \quad \Sigma x ^ { 2 } = 6.19$$
- Test at the \(5 \%\) significance level whether the farmer's claim is justified, assuming a normal distribution.
- Find a 95\% confidence interval for the population mean yield for plants grown in the new soil.