STA 402S98 Assignment 9: Quiz in tutorial March 21

Read pages 958-976. For a single-factor random effects model, the only hypothesis test for which you are responsible is the one for testing sigma-squared-sub-mu equals zero (computationally, this is exactly the same as a one-factor fixed effects ANOVA). The only confidence interval for which you are responsible is the one for µ. ; see formulas (24.13) and (24.15). Notice that a lot of fairly complicated stuff is being skipped. Your primary task for this section is to understand the model and be able to prove things about expected values and variances.

1. Prove formulas 24.2c, 24.2d, 24,4, 24.6, 24.7 and 24.12 from the text.

2. Do problems 24.3, 24.24 and 24.25.

3. You want to estimate the population mean Grade 8 math performance for all primary schools in Ontario. You will randomly sample r schools, and then from each school you will randomly sample n students and test them. Given that you are only authorized to test a total of 100 students, how many schools should you select so that your estimate will have maximum accuracy? Hint: Do this problem after you do problem 2.