(a) Scientists have used Mongolian gerbils when conducting neurological research
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Question
(a) Scientists have used Mongolian gerbils when conducting neurological research. A certain breed of these gerbils was crossed and gave progeny of the following colors: Is this data consistent with the 1: 2: 1 ratio predicted by a certain genetic model? Use a chi-square test at alpha = 0.05. (b) Suppose that scientists suspected that brown gerbils were more likely to produce progeny with birth defects than black progeny. The progeny of the black and brown gerbils in the previous part were al assessed for birth defects. The results were as follows: Based on this table, conduct a hypothesis test to assess whether a gerbil having progeny with birth defects is independent of being black or brown. Use alpha = 0.01.Explanation / Answer
a) here null hypothesis: proportion of black , brown and white progeny color is 1:2:1.
alternate hypothesis proportion of black , brown and white progeny color is differnt from 1:2:1.
for 2 degree of freedom and 0.05 level ; criitcal value =5.991
applying chi square goodness of fit test:
as test stat 3.8085 is less then critical value we can not reject null hypothesis and conclude that data is consistent with 1:2:! predicted ratio.
b)
null hypothesis: progeny with birth defect is independent of color.
alternate hypothesis:progeny with birth defect is dependent of color.
here at 1 degree of freedom and 0.01 level ; critical value =6.635
applying chi square test of independence on above data
as test stat chi square is less then critical value ; we can not reject null hypothesis that progeny with birth defect is independent of color.
observed Expected Chi square Type Probability O E=total*p =(O-E)^2/E black 0.250 40.000 35.25 0.64 brown 0.500 59.000 70.50 1.88 white 0.2500 42.000 35.25 1.29 1 141 141 3.8085Related Questions
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