9 A random sample of five metal rods produced by a machine is taken. Each rod is tested for hardness. The results, in suitable units, are as follows. $$\begin{array} { l l l l l } 524 & 526 & 520 & 523 & 530 \end{array}$$ Assuming a normal distribution, calculate a \(95 \%\) confidence interval for the population mean. Some adjustments are made to the machine. Assume that a normal distribution is still appropriate and that the population variance remains unchanged. A second random sample, this time of ten metal rods, is now taken. The results for hardness are as follows. $$\begin{array} { l l l l l l l l l l } 525 & 520 & 522 & 524 & 518 & 520 & 519 & 525 & 527 & 516 \end{array}$$ Stating suitable hypotheses, test at the \(10 \%\) significance level whether there is any difference between the population means before and after the adjustments.