Let's continue with the test data set of Problem 3. The factory's goal remains (as in lectures) that Η₀:μ = 10, and based on new test data we wish (again) to find out whether the machine should be adjusted.
(a) Does the value of the parameter value μ =10 following the null hypothesis belong to the 2 - sided confidence interval calculated in Problem 3?
(b) Create a t-test statisics corresponding to this situation and calculate its value.
(c) Calculate the p-value of the test.
(d) The factory did not want to adjust the device unnecessarily except at most once in 100 cases. What significance level corresponds to this if the null hypothesis is "no need to adjust the machine" and adjustment corresponds to the rejection of the null hypothesis? Would it be necessary to adjust the machine in this case (i.e., to reject the null hypothesis) ?