want you to do the following problem by hand. The problem is a two way Anova with interaction. There are two treatments on the vertical axis (teaching methods), and two treatments on the horizontal axis (morning or evening class). That is to say, J which goes from 1 to b, goes from 1 to 2, and i which goes from 1 to a, goes from 1 to 2. The dependent variable is the score on the test. The value of the grand mean is equal to 150, 1 is equal to -5, 2 is equal to +5. Also 1 is equal to -3, 2 is equal to +3. There is no interaction effect . The standard deviation is equal to 3. Now use the unrealistic process of creating the three random variables in each of the four cells. Make the first observation within each cell, three less than the cell mean, the second observation equal to the cell mean , and the third observation in each of the four cells, three more than the cell mean. a. Construct the data table b. Construct the ANOVA table, finding the F values associated with the main effects, as well as the interaction effects. Set up the three null hypothesis and come to the appropriate conclusions. c. Now determine if the Tukey test would have found significant teaching effects. d. Now determine if the Tukey test would have found significant time of days effect. 3) Now do the problem over again, except let the interaction effect for 11 to be + 4, which forces 12 to be -4, and 21 to be -4, and 22 to be +4. a. the same b. the same c. Use the tukey test to check for significant interaction effect.

4) Describe a situation in which the use of a two way ANOVA with interaction would be appropriate to analyze the problem.