A random sample of five metal rods produced by a machine is taken. Each rod is tested

<p style="text-align: justify;">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.</p><p style="text-align: justify;">524 526 520 523 530</p><p style="text-align: justify;"><br></p><p style="text-align: justify;">i. Assuming a normal distribution, calculate a 95% confidence interval for the population mean.</p><p style="text-align: justify;">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.</p><p style="text-align: justify;"><img src="https://dsd5zvtm8ll6.cloudfront.net/si.question.images/images/question_images/1633/4/1/9/581615c013dc994d1633419583761.jpg" class="fr-fic fr-dib" width="54.85%" style="width: 54.85%;" height="54"></p><p style="text-align: justify;"><br></p><p style="text-align: justify;">ii. Stating suitable hypotheses, test at the 10% significance level whether there is any difference between the population means before and after the adjustments.</p>