91Ó°ÊÓ

a. The null hypothesis to test the overall significance of the model will be to check if all the β parameters are zero or not. Mathematically, H₀:${\mathrm{β}}_0={\mathrm{β}}_1={\mathrm{β}}_2={\mathrm{β}}_3={\mathrm{β}}_4={\mathrm{β}}_5=0.$.

b. The null hypothesis to test whether task performance score (y) and conscientiousness score (x₁) are curvilinearly related will be to check if all the β parameters representing theare zero or not. Mathematically, H₀:${\mathrm{β}}_2={\mathrm{β}}_5=0.$.

c. The null hypothesis to test whether the curvilinear relationship between task performance score (y) and conscientiousness score (x₁) depends on job complexity (x₂) will be to check if all the β parameters representing (x₁)²the interaction terms are zero or not. Mathematically, H₀:${\mathrm{β}}_4={\mathrm{β}}_5=0.$.

d. In part a, F-test would be conducted to check the overall significance of the model. The reduced model in this part would be$E\left(y\right)={\mathrm{β}}_0+{\mathrm{β}}_1{x}_1+{\mathrm{β}}_2{\left(x_1\right)}^2+{\mathrm{β}}_3{x}_2+{\mathrm{β}}_4{x}_1{x}_2+{\mathrm{β}}_5{\left(x_1\right)}^2{x}_2$ . In part b, t-test would be conducted to check the existence of curvilinear relationship between (y) and (x₁). The reduced form model would be$E\left(y\right)={\mathrm{β}}_0+{\mathrm{β}}_1{x}_1+{\mathrm{β}}_2{\left(x_1\right)}^2+{\mathrm{β}}_3{x}_2+{\mathrm{β}}_4{x}_1{x}_2$. In part c, t-test would be conducted to check if interaction between variables exists or not. The reduced form model would berole="math" $E\left(y\right)={\mathrm{β}}_0+{\mathrm{β}}_1{x}_1+{\mathrm{β}}_2{\left(x_1\right)}^2+{\mathrm{β}}_3{x}_2$.