We are interested in comparing achievement for three types of training, but we are concerned that the aptitude may affect the achievement. For a sample of subjects, y= achievement, x = aptitude, and z = training group (one, two, three) were collected. Use SAS output to answer the following questions. For all your hypothesis testing use ? = 0.05.

(a). Write out an appropriate model for this scenario.

(b) Specify appropriate null and alternate hypotheses for testing for a linear relationship between achievement and aptitude. Report values for the F-statistic, degrees of freedom, and p-value and state the conclusion of this test.

(c) Specify appropriate null and alternate hypotheses for testing whether the training has a difference in average achievement. Report the values for the F-statistic, degrees of freedom, and p-value and state the conclusion of this test.

The GLM Procedure Dependent Variable: y Sum of Source OF Mean Square F Value Pr > F Model 3 2175 131579 758 450326 11.73 4,0001 Error Comected Toml 3956.000000 R-Square Coelf Var Rool MIST. 0575165 21 97120 3.035921 35.08000 Mean Square F Value I 1 1567 358951 1567 359954 3.25 Training 1 0104 SOUTH Type ITISS Mean Square F Vale Pr > F 1855 351579 1855.350579 28.70 COMI Training 707 1916 353 .995812 0.0104