$1.$ Path$-$goal leadership theory suggests leaders to adjust leadership style or behavior based on follower$$s characteristics and work environment. Conduct an analysis to test if the effect of supportive leadership on job satisfaction depends on teachers$$ experience. The data are available in the file named PathGoal.sav. $(10$ points$)$

a$.$ State the null and alternative hypotheses of the moderator, both mathematically and in words. $(2$ points$)$

b$.$ Is the effect of supportive leadership on teacher$$s satisfaction significant? Explain. $(2$ points$)$

c$.$ Does the effect of supportive leadership on teacher$$s satisfaction depend on years of experience? Explain. $(2$ points$)$

d$.$ What is the variance attributable to the interaction variable? $(2$ points$)$

e$.$ Develop a chart to show the effect of the interaction variable. Make sure you discuss the chart. $(2$ points$)$