Lily, a statistician, decided to have a pet in her home, but she had a hard time making up her mind between cat and dog. A friend told her that the average lifespan of dogs is 5 years longer than that of cats. She was more of a cat person; however, if her friend's theory was true, she would get a dog. In order to verify her friend's theory, she investigated pets that had recently passed away and found the lifespan of 12 dogs and 15 cats.
(Sample of the lifespan of dog)
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(Sample of the lifespan of cat)
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Dog
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Lifespan(years)
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Cat
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Lifespan(years)
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1
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5.3
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1
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8.4
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2
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13.6
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2
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10.7
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3
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15
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3
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9.5
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4
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14
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4
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9.8
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5
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11
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5
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13
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6
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9.4
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6
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8.6
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7
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12.2
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7
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12
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8
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12.8
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8
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8
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9
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13.8
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9
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10.5
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10
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10
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10
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6.4
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11
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8.5
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11
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12.7
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12
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15.5
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12
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6.8
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13
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15
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14
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11
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15
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11.1
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In addition to these data, she also learned from a doctor in an animal hospital that the lifespan of dogs is normally distributed with standard deviation equal to 4 years and that of cat is equal to 3 years. Then she went on to test her friend's theory using all the information she collected.
1.
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Determine the null hypothesis:
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Null Hypothesis: The average difference between the lifespan of dogs and cats is 5 years
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2.
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Substitute the information into the formula:
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, , , , , ,
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,
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This statistical test provides evidence that the null hypothesis is false, so we reject the null hypothesis.
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