Slide Teste de Aderencia-2021 2

❚❡st❡ ❞❡ ❆❞❡rê♥❝✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ ❇❛❤✐❛ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ✷✵✷✶✳✷ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✶ ✴ ✾ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ◆❛ ❧✐t❡r❛t✉r❛✱ ❡①✐st❡♠ ✈ár✐❛s ♠❛♥❡✐r❛s ❞❡ r❡❛❧✐③❛r ❚❡st❡s ❞❡ ❆❞❡✲ rê♥❝✐❛✱ ♣♦ré♠ ♥❡st❡ t❡①t♦ s❡rá ❛♣r❡s❡♥t❛❞♦ ❛♣❡♥❛s ♦ ❚❡st❡ ◗✉✐✲ ◗✉❛❞r❛❞♦ ✭χ✷✮✳ ❊st❡s t❡st❡s t❛♠❜é♠ sã♦ ❝❤❛♠❛❞♦s ❞❡ ❚❡st❡s ❞❡ ❇♦♥❞❛❞❡ ❞❡ ❆❥✉s✲ t❛♠❡♥t♦✳ ❆ ❞✐str✐❜✉✐çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ✉t✐❧✐③❛❞❛ é ❛ ◗✉✐✲◗✉❛❞r❛❞♦✳ ❚❡st❡ ❞❡ ❛❞❡rê♥❝✐❛ s❡r✈❡ ♣❛r❛ ✈❡r✐✜❝❛r ❛ ❛❞❡q✉❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ♠♦❞❡❧♦ ♣r♦❜❛❜✐❧íst✐❝♦ ♣r♦♣♦st♦ ♣❛r❛ ✉♠❛ ✈❛r✐á✈❡❧✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✷ ✴ ✾ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ❉❛❞❛ ✉♠❛ ❛♠♦str❛ ❛❧❡❛tór✐❛ ❞❡ t❛♠❛♥❤♦ ♥✱ ♦❜s❡r✈❛❞❛ ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❳ ✱ ♥♦ss♦ ♦❜❥❡t✐✈♦ é t❡st❛r✿ ❍✵ : ❳ t❡♠ ❞✐str✐❜✉✐çã♦ ❢ ❍✶ : ❳ ♥ã♦ t❡♠ ❞✐str✐❜✉✐çã♦ ❢✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✸ ✴ ✾ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ♥ ♦❜s❡r✈❛çõ❡s ✐♥❞❡♣❡♥❞❡♥t❡s ❞❡ ✉♠❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❳ ❝♦♠ ❢✉♥çã♦ ❞❡ ❞✐str✐❜✉✐çã♦ ♥ã♦ ❡s♣❡❝✐✜❝❛❞❛✳ ❈❛❞❛ ♦❜s❡r✈❛çã♦ é ❝❧❛ss✐✜❝❛❞❛ ❡♠ ✉♠❛ ❞❛s ❦ ❝❛t❡❣♦r✐❛s✱ ❞❡ ❢♦r♠❛ q✉❡ ❛ s❡❣✉✐♥t❡ t❛❜❡❧❛ ❞❡ ❝♦♥t✐♥❣ê♥❝✐❛ ♣♦❞❡ s❡r ❝♦♥str✉í❞❛✳ ❱❛r✐á✈❡❧ ❈❛t❡❣♦r✐❛s ✶ ✷ ✸ ✳✳✳ ❦ ❋r❡q✉ê♥❝✐❛ ❖❜s❡r✈❛❞❛ ❖✶ ❖✷ ❖✸ ✳✳✳ ❖❦ ❖✐ r❡♣r❡s❡♥t❛ ❛ ❢r❡q✉ê♥❝✐❛ ♦❜s❡r✈❛❞❛ ♥❛ ❝é❧✉❧❛ ✐✱ ♣❛r❛ ✐ = ✶, ✷, ✸, · · · , ❦ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✹ ✴ ✾ a Teste de Qui-Quadrado (x) de Aderéncia eo As hipoteses estatisticas a serem testadas sdo: Ho: A variavel X segue o modelo proposto; Hy: A variavel X nao segue o modelo proposto. k (O; _ E;)? Xeal = >= ~ XS . a w=1 MAT023 2021.2 5/9 ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ◆♦t❛çã♦ ❊✐✿ ❢r❡q✉ê♥❝✐❛ ❡s♣❡r❛❞❛ ♥❛ ✐✲és✐♠❛ ❝❛t❡❣♦r✐❛✱ ❞❛❞❛ ♣♦r ❊✐ = ♥♣✐❀ ♣✐ ❂ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ ❝❛t❡❣♦r✐❛ ✐✱ s✉♣♦♥❞♦ q✉❡ ❍✵ é ✈❡r❞❛❞❡✐r❛✳ υ = ❦ − ✶ s❡ ❛s ❢r❡q✉ê♥❝✐❛s ❡s♣❡r❛❞❛s ♣✉❞❡r❡♠ s❡r ❝❛❧❝✉❧❛❞❛s s❡♠ ♣r❡❝✐s❛r ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ❞❛ ❞✐str✐❜✉✐çã♦✳ P❛r❛ ✉♠ ❞❛❞♦ α✱ r❡❥❡✐t❛r ❛ ❤✐♣ót❡s❡ ♥✉❧❛ s❡ χ✷ ❝❛❧ > χ✷ α;υ✳ ❖✉ r❡❥❡✐t❛r ❛ ❤✐♣ót❡s❡ ♥✉❧❛ s❡ ♣ − ✈❛❧♦r < α✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✻ ✴ ✾ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ❆ ❞✐str✐❜✉✐çã♦ q✉✐✲q✉❛❞r❛❞♦ é ❝♦♥tí♥✉❛ ❡ ❛ss✐♠étr✐❝❛ ❡ ❝♦♠♦ ❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ♣❛❞r♦♥✐③❛❞❛ t❛♠❜é♠ é t❛❜❡❧❛❞❛✳ P✭χ✷✶✵ ≥ χ✷✭✵✱✵✺❀✶✵✮✮ ❂ P✭χ✷✶✵ ≥ ✶✽✱✸✵✼✮ ❂ ✵✱✵✺✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✼ ✴ ✾ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ✶ ◗✉❛♥❞♦ ♦ ♥ú♠❡r♦ ❞❡ ❝❛t❡❣♦r✐❛s ❢♦r ✐❣✉❛❧ ❛ ❞♦✐s ✭❦❂✷✮ ❛s ❢r❡q✉ê♥✲ ❝✐❛s ❡s♣❡r❛❞❛s ❞❡♥tr♦ ❞❡ ❝❛❞❛ ❝❛t❡❣♦r✐❛ ❞❡✈❡♠ s❡r ✐❣✉❛✐s ♦✉ s✉♣❡✲ r✐♦r❡s ❛ ✺✳ ✷ ◗✉❛♥❞♦ ❦ > ✷✱ ♥ã♦ ❞❡✈❡ t❡r ♠❛✐s ❞❡ ✷✵✪ ❞❛s ❝❛t❡❣♦r✐❛s ❝♦♠ ❢r❡q✉ê♥❝✐❛s ❡s♣❡r❛❞❛s ♠❡♥♦r❡s q✉❡ ✺ ❡ ♥❡♥❤✉♠❛ ❢r❡q✉ê♥❝✐❛ ❡s♣❡✲ r❛❞❛ ✐❣✉❛❧ ❛ ③❡r♦✳ ✸ ◗✉❛♥❞♦ ❛s ❝❛t❡❣♦r✐❛s ❛♣r❡s❡♥t❛r❡♠ ♣❡q✉❡♥❛s ❢r❡q✉ê♥❝✐❛s ❡s♣❡r❛✲ ❞❛s ❡❧❛s ♣♦❞❡♠ s❡r ❝♦♠❜✐♥❛❞❛s ❝♦♠ ♦✉tr❛s ❝❛t❡❣♦r✐❛s✱ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ♦ s❡♥t✐❞♦ ❞♦ tr❛❜❛❧❤♦ s❡❥❛ ❝♦♥s❡r✈❛❞♦✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✽ ✴ ✾ ❊①❡r❝í❝✐♦ ✶ ❯♠❛ ✐♥❞ústr✐❛ r❡❣✐str❛✱ ❡♠ ❝❛❞❛ s❡♠❛♥❛✱ ♦ ♥ú♠❡r♦ ❞❡ ❞✐❛s ❡♠ q✉❡ ♦❝♦rr❡♠ ❛❝✐❞❡♥t❡s ❞❡ tr❛❜❛❧❤♦✳ P❛r❛ ✉♠❛ ❛♠♦str❛ ❞❡ ✷✵✵ s❡♠❛♥❛s✱ ✈❡r✐✜q✉❡ s❡ ♦s ❞❛❞♦s ❛♣r❡s❡♥t❛❞♦s ❛ s❡❣✉✐r✱ ❛❞❡r❡♠ ❛♦ ♠♦❞❡❧♦ ❇✐♥♦♠✐❛❧ ❝♦♠ ♣❛râ♠❡tr♦s ♥ ❂ ✺ ❡ ♣ ❂ ✵✱✷✳ ✭❯s❡ α ❂ ✶✵✪✮✳ ◆ú♠❡r♦ ❞❡ ❞✐❛s ❝♦♠ ❛❝✐❞❡♥t❡s ✵ ✶ ✷ ✸ ✹ ✺ ❋r❡q✉ê♥❝✐❛ ✻✹ ✺✻ ✹✵ ✷✹ ✽ ✽ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✾ ✴ ✾