A geneticist claims that four species of fruit files should appear in the ratio 1:3:3:9. Suppose that a sample of 2000 files contained 110, 345, 360, and 1185 files of each species, respectively. Is there sufficient evidence to reject the geneticist's claim?
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Very tough one
Explanation:
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Given:
Ratio = 1:3:3:9
Sample size = 2000
Samples = 110, 345, 360, and 1185
To Find:
Evidence to reject geneticist's claim.
Total fruits = 1 + 3 + 3 + 9 = 16
As per the geneticist expected number of fruit flies of each species = 1/16(2000) = 125.3/16(2000) = 375.3/16(2000) = 375.9/16(2000)
= 1125
According to Chi Square test -
x² = ( obs - exp)²/exp
= ( 110 - 125)²/125 + ( 345 - 375)²/375 + ( 360 - 375)²/375 + ( 1185 - 1125)²/1125
= (15)²/125 + (30)²/375 + (15)²/375 + (60)²/1125
= 8
with df = 4 - 1 = 3, and P( x² > 8) = 0.0460.
With a P-value it is small. (0.0460 < 0.05).
Answer: Thus, there is sufficient evidence at the 5% significance level to reject the claim.
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