For each problem, you will have to determine the design. Your design choices are ANCOVA, Nested Design, Random Effects, Fixed Effects, and Mixed Effects (in that order). So, if it is a Nested Design with fixed treatments, you will answer Nested Design, not Fixed Effects. For each of the problems include interaction terms where appropriate. You will fill in the table as you did for Quiz 3. In addition determine if each component is fixed/random/NA. Assume all necessary assumptions are valid. If you decide ANCOVA, you will have Full Table, Reduced Model I Table, and Reduced Model II Table.

1) Consider the following situation There is a study looking at the uptakes of uorescently labelled protein in rat kidneys. The researcher wanted to know if there were differences in the way his two technicians were performing the procedure. The rst technician chose three rats. The second technician then choose three rats on her own. Each technician then measured the protein uptake in 10 random locations in the kidneys of each rat. Complete the following ANOVA table, including the correct DF's. Source 55 df MS Fixed/ Random F 2) Consider the following situation A textile company weaves a fabric on a large number of loms. It would like the looms to be homogeneous so it obtains a fabric of uniform strength. The process engineer suspects that there mayr be signicant variations in strengths between looms. To investigate this. the engineer selects four looms at random and makes four strength dterminations on the fabric manufactured on each Complete the following ANOVA table, including the correct DF's. Source 55 df Ms Fined/Random F 3) Consider the following situation We are investigating differences that may exist between four different potential math text books. Ten students each are chosen to study from one of the textbooks. At the end of the class. a math test is given. Because the students may have different math abilities, we have a rating of each student's math ability (from 1-20) from the student's teachers. Complete the following ANOVA table. including the correct DF's. Source 55 df M5 Fixed/Random F