STATISTICAL INDEPENDENCE SP '11

# STATISTICAL INDEPENDENCE SP '11 - Owns P Y PROBABILIT L...

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STATISTICAL INDEPENDENCE To establish if two events are statistically independent—or not— you must compare one simple probability with one conditional probability . If the two probabilities are equal , the two events are statistically independent. 1. Are dog ownership and cat ownership statistically independent events, based on this data from 800 families? Owns Dog No Dog Total Owns Cat 180 120 300 No Cat 160 340 500 Total 340 460 800 ( 29 ( 29 % 60 300 180 : % 5 . 42 800 340 : = = = = Cat Owns Dog Owns P Y PROBABILIT L CONDITIONA Dog Owns P Y PROBABILIT SIMPLE The two events are not statistically independent. The event of owning a cat changes the probability of owning a dog. You will get the same conclusion if you start with “Owns Cat” instead of “Owns Dog”: ( 29 ( 29 % 941 . 52 340 180 : % 5 . 37 800 300 : = = = = Dog Owns Cat
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Unformatted text preview: Owns P Y PROBABILIT L CONDITIONA Cat Owns P Y PROBABILIT SIMPLE 2. Are DVD player ownership and TV ownership statistically independent events, based on this data from 800 families? Owns TV No TV Total Owns DVD player 510 90 600 No DVD player 170 30 200 Total 680 120 800 ( 29 ( 29 % 75 680 510 : % 75 800 600 : = = = = TV Owns player DVD Owns P Y PROBABILIT L CONDITIONA player DVD Owns P Y PROBABILIT SIMPLE These two events are statistically independent . The event of a family owning a TV does not affect the probability of a family owning a DVD player. You will get the same conclusion if you start with “Owns TV” instead of “Owns DVD player”: try it. Math 40 SP ‘11...
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