Exercises for Wed 12 November

1. On Wed 7th I (somewhat quickly) went through the relevant parts of Ch 8, including the Neyman-Pearson lemma, and stressed the importance of the result that Z_n = - 2 \log LR_n tends to \chi^2_df, under the null hypothesis, where df = dim(a priori) - dim(H_0).

2. Exercises for next week: First the following sample size calculations. (a) Assume that the heights of men and women above the age of twenty in Norway follow distributions N(xi_m,sigma^2) and N(xi_w,sigma^2), with known sigma = 9 cm, and that you are to test the hypothesis (though you already know it doesn't hold up) that the two mean heights are identical. You sample n men and n women and measure them gently, from head to toe. How big must n be, in order for you to be 99% sure that your 1% level test will detect the difference, if the real difference between the means is 13 cm? (b) You visit the nearest fødeavdeling and observe n newborns, noting their gender, and set up at 1% level test for the hypothesis that p = 0.50, where p is the probability of a girl. How many babies must be examined, before you can be 99% sure that your test detects that the hypothesis is wrong, if the real p is 0.485 (which is close to what I believe the real value is)? -- Then, from Ch 8: 5, 8, 9, 13, 17.

3. We shall organise another "extra hour" for Wed 12 Nov, from 13:15, to find time for doing exercises and perhaps discuss other details. I will tell you Wed morning where we are then going to meet at 13:15.