Consider two different normal distributions for which both the means 1 and 2 and the variances 2 1 and 2 2 are unknown, and suppose that it is desired to test the following hypotheses: H0: 2 1 2 2, H1: 2 1 > 2 2. Suppose further that a random sample consisting of 16 observations for the first normal distribution yields the values 16 i=1 Xi = 84 and 16 i=1 X2 i = 563, and an independent random sample consisting of 10 observations from the second normal distribution yields the values10 i=1 Yi = 18 and 10 i=1 Y 2 i = 72. a. What are the M.L.E.s of 2 1 and 2 2? b. If an F test is carried out at the level of significance 0.05, is the hypothesis H0 rejected or not?

Chapter 11 --- Means (Sampling Distribution, Confidence Intervals, Hypothesis Tests) Sampling Distribution of a Sample Mean Example 1: The Arm and Hammer Company wants to ensure that their laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount per container is 100 fluid ounces and the standard...