AlHadi College Statistics Worksheet

For each of the three descriptions below, say whether or not each of factorial, with replication, and balancedapply or not, and specifically how you could tell.a) An ANOVA is performed to see how effective different methods of studying are, and how much extra timespent helps. Students studied by either primarily going over old exams, reading notes, or reading the text; andthey studied for either two, five, or ten hours. The forty-five students were assigned at random so that therewere five in each of the combinations of studying strategies and time.b) An ANOVA is performed to see how effective different methods of studying are, and how much extra timespent helps. Students studied by either primarily going over old exams, reading notes, or reading the text; andthey studied for either two, five, or ten hours. The sixteen students were assigned at random so that four spenttwo hours using the text, four spent two hours using the notes, four spent two hours using the old exams, twospent five hours using text, and two spent ten hours using the text.c) An ANOVA is performed to see how effective different methods of studying are, and how much extra timespent helps. Students were assigned to study by either primarily going over old exams, reading notes, orreading the text; and they studied for either two, five, or ten hours. The nine students were assigned at randomso that there was one in each of the combinations of studying strategies and time.2) Questions 2 uses the following setting – Seven different types of material (labeled A-G) were sent out to asample of 13 laboratories for stress testing (since different laboratories use different testing methods), with fourcopies of each sample being sent to each lab. The PROC GLM code used was:PROC GLM;CLASS lab material;MODEL stress = lab material lab*material;RANDOM lab lab*material;RUN;And the output was:Sum ofSource DF Squares Mean Square F Value Pr > FModel 90 322913.2482 3587.9250 177.01 <.0001Error 273 5533.5800 20.2695Corrected Total 363 328446.8282Source DF Type III SS Mean Square F Value Pr > Flab 12 30328.0547 2527.3379 124.69 <.0001material 6 268778.0771 44796.3462 2210.03 <.0001lab*material 72 23807.1165 330.6544 16.31 <.0001Source Type III Expected Mean Squarelab Var(Error) + 4 Var(lab*material) + 28 Var(lab)material Var(Error) + 4 Var(lab*material) + Q(material)lab*material Var(Error) + 4 Var(lab*material)a) What null hypothesis is being tested by the material line in the Type III table (the F-value of 2210.03).Carefully state the null and alternate hypothesis and your conclusion at the =0.05 level.b) Find the value of the F statistic for testing H0:2lab =0 against HA:2lab >0, and test that hypothesis at the=0.05 level. (The critical value can be found using qf in R or a web-page for calculating F-critical values suchas http://www.biokin.com/tools/f-critical.html; similarly, the p-value could be found using pf inR or an F distribution calculator on line. In any case, make sure you are using it correctly to get the probabilityin the end of the distribution you want).