5. When Y,,Y,..,Y, is a random sample from N(u,0). we learned in class that the Y-u statistic T = has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard...

Extracted text: 5. When Y,,Y,..,Y, is a random sample from N(u,0). we learned in class that the Y-u statistic T = has t distribution with n-1 degrees of freedom, where Y and S are the sample mean and sample standard deviation, respectively. Write out the form of T² and show algebraically that T can be written as the ratio of two independent z random variables, each divided by their respective degrees of freedom. What is, therefore, the distribution of T? (5 pts.)