2. One-sample t-test: Take the same setting as above but now with o2 also unknown. We want to conduct a one-sided hypothesis test of the following form Ho: μ =μο vs H: μ> μο Look through the calculations in class. Notice that the null no longer specifies the distribution of the sample (since it doesn't specify a variance). Discuss what can be done here? Look at the form of the test statistic once we had normalised it. We did this by dividing by the standard deviation, but we don't know this now. Can we divide instead by it's estimator? Note: Functions of the test statistic that no-longer have a distribution that depends on the parameters that may be unknown are called pivots. we will see more of these later in week 8. 4. Take the setting of Question 2 from Tutorial sheet 4. However, now suppose that we instead wish to test: H₁: (μ,0²) = (0, 4), vs H₁: (μ,0²) ‡ (0, 4) Assuming that you have a sample of size n = 50 and observe n Στ = 10 2 i=1 i=1 Use Wilk's Theorem to test the stated hypothesis at size a = 0.05. x² = 250