-Formulate the null and alternative hypothesis-Compute value of the test statistic-what is the p-value? What do you conclude-find the critical value-using the critical value approach and your answer in the previous question, null hypothesis should

Problem 1: A machine cuts steel to length for nails. The mean length of a nail is 43 millimeters. There is concern that the settings of the machine producing the nails have changed. To test the claim, twelve nails (n = 12) were sampled. The mean of the sample is 41.5 and the sample standard deviation is 1.784. At the 0.05 significance level, can we conclude that the settings of the machine have changed