Slide Teste de Independencia-2021 2

❚❡st❡ ❞❡ ■♥❞❡♣❡♥❞ê♥❝✐❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❛ ❇❛❤✐❛ ■♥st✐t✉t♦ ❞❡ ▼❛t❡♠át✐❝❛ ❡ ❊st❛tíst✐❝❛ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ✷✵✷✶✳✷ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✶ ✴ ✼ ❚❡st❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❖ t❡st❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ◗✉✐✲◗✉❛❞r❛❞♦ é ✉s❛❞♦ ♣❛r❛ ✈❡r✐✜❝❛r s❡ ❡①✐st❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❞✉❛s ✈❛r✐á✈❡✐s ♠❡❞✐❞❛s ♥❛s ♠❡s♠❛s ✉♥✐❞❛❞❡s ❡①♣❡r✐♠❡♥t❛✐s✳ ❆s ❤✐♣ót❡s❡s ❛ s❡r❡♠ t❡st❛❞❛s sã♦✿ ❍✵ : ❆ ❡ ❇ sã♦ ✈❛r✐á✈❡✐s ✐♥❞❡♣❡♥❞❡♥t❡s ❍✶ : ❆s ✈❛r✐á✈❡✐s ❆ ❡ ❇ ♥ã♦ sã♦ ✐♥❞❡♣❡♥❞❡♥t❡s✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✷ ✴ ✼ ❚❡st❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❊①❡♠♣❧♦✿ ❉❡s❡❥❛✲s❡ ✈❡r✐✜❝❛r s❡ ❡①✐st❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛ r❡♥❞❛ ❡ ♦ ♥ú♠❡r♦ ❞❡ ✜❧❤♦s ❡♠ ❢❛♠í❧✐❛s ❞❡ ✉♠❛ ❝✐❞❛❞❡✳ ❋♦r❛♠ ❡s❝♦❧❤✐❞❛s ❛♦ ❛❝❛s♦ ✷✺✵ ❢❛♠í❧✐❛s ❡ ♦ r❡s✉❧t❛❞♦ ❢♦✐✿ ❚❛❜❡❧❛ ✶✿ ❋❛♠í❧✐❛s ♣♦r ◆ú♠❡r♦ ❞❡ ❋✐❧❤♦s ❡ ❘❡♥❞❛ ❘❡♥❞❛ ✭❘✩✮ ◆ú♠❡r♦ ❞❡ ❋✐❧❤♦s ❚♦t❛❧ ✵ ✶ ✷ > ✷ ♠❡♥♦s ❞❡ ✷✵✵✵ ✶✺ ✷✼ ✺✵ ✹✸ ✶✸✺ ✷✵✵✵ ❛ ✺✵✵✵ ✷✺ ✸✵ ✶✷ ✽ ✼✺ ✺✵✵✵ ♦✉ ♠❛✐s ✽ ✶✸ ✾ ✶✷ ✹✵ ❚♦t❛❧ ✹✽ ✼✵ ✼✶ ✻✶ ✷✺✵ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✸ ✴ ✼ ❚❡st❡ ❞❡ ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❙❡ ❆ ❡ ❇ ❢♦r❡♠ ✐♥❞❡♣❡♥❞❡♥t❡s✱ q✉❛♥t❛s ♦❜s❡r✈❛çõ❡s ❡s♣❡r❛✲s❡ t❡r ❡♠ ❝❛❞❛ ❝❛s❡❧❛ (✐, ❥ )❄ ◆❡st❡ ❝❛s♦✱ P(❆✐ ∩ ❇❥ ) = ♣✐❥ = P(❆✐)P(❇❥ ) ✐ = ✶, . . . , r ❥ = ✶, . . . , ❝ ✳ ◆ã♦ ♠❛✐s ❞❡ ✷✵✪ ❞❛s ❢r❡q✉ê♥❝✐❛s ❡s♣❡r❛❞❛s sã♦ ✐♥❢❡r✐♦r❡s ❛ ✺✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✹ ✴ ✼ a Teste de independéncia Tr (a 2 i y a pee ee) Y w=1 g=1 tem distribuigdéo aproximadamente Quz — Quadrado com (r —1)(c —1) graus de liberdade. By =n Me Bd _ HM taleegyr nn n j=l,...,c MAT023 2021.2 5/7 ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭χ✷✮ ❞❡ ❆❞❡rê♥❝✐❛ ❋✐❣✉r❛ ✶✿ ❚❡st❡ ❞❡ ◗✉✐✲◗✉❛❞r❛❞♦ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✻ ✴ ✼ ❊①❡r❝í❝✐♦ ✶ ◆♦ ❈♦♥❣r❡ss♦ ❆♠❡r✐❝❛♥♦✱ ❣r✉♣♦s ❞❡ ❞❡♠♦❝r❛t❛s ❡ r❡♣✉❜❧✐❝❛♥♦s ✈♦t❛r❛♠ ❡♠ ✉♠ ♣r♦❥❡t♦ ❞❡ ✐♥t❡r❡ss❡ ♥❛❝✐♦♥❛❧ ❝♦♠♦ ❡stá ♥❛ t❛❜❡❧❛ ❛ s❡❣✉✐r✳ ❆♦ ♥í✈❡❧ ❞❡ ✺✪✱ t❡st❛r ❛ ❤✐♣ót❡s❡ ❞❡ ♥ã♦ ❤❛✈❡r ❞✐❢❡r❡♥ç❛ ❡♥tr❡ ♦s ❞♦✐s ♣❛rt✐❞♦s✱ ❝♦♠ r❡❧❛çã♦ ❛ ❡ss❡ ♣r♦❥❡t♦✳ ❱♦t♦s P❛rt✐❞♦ ❆ ❢❛✈♦r ❈♦♥tr❛ ■♥❞❡❝✐s♦s ❉❡♠♦❝r❛t❛s ✽✺ ✼✽ ✸✼ ❘❡♣✉❜❧✐❝❛♥♦s ✶✶✽ ✻✶ ✷✺ ❘✿ ❍✐♣ót❡s❡ ♥✉❧❛ é r❡❥❡✐t❛❞❛✱ ❘❡❣✐ã♦ ❝rít✐❝❛ ❬✺✱✾✾✶❀ ∞✮ ❡ χ✷ ❝❛❧ ❂ ✾✱✼✷✼✻✳ ✭❉❊st✴❯❋❇❆✮ ▼❆❚✵✷✸ ✷✵✷✶✳✷ ✼ ✴ ✼