Humans can be categorized based on their blood group into 4 categories, namely,

Question

Humans can be categorized based on their blood group into 4 categories, namely, 0, A, B, and AB. Additionally, the presence or absence of Rh antigens is also useful to divide humans into +ve and -ve blood group categories. Consequently, humans can belong to any of the 8 possible combinations, namely, 0+, 0-, A+, A-, B+, B-, AB+, and AB-. In a sample of 150 people in Rh +ve category, 69 had 0 group, 61 had A group, 15 had B group and 5 had AB group. In a sample of 100 people in the Rh -ve group, 44 had 0 group, 39 had A group, 9 had B group and 8 had AB group. Can you conclude that the distribution of the letter types (O, A, B, and AB) is different for people with Rh +ve and Rh -ve types? State your null hypothesis, value of your test statistic, p-value and conclusion.

Explanation / Answer

here we will use chi square test for independence.

null hypothesis: distribution of letter type is independent of Rhesus Group

alternate hypothesis:distribution of letter type is not independent of Rhesus Group

here degree of freedom =(row-1)*(column-1) =(2-1)(4-1) =3

value of test stat =2.670

p value for above tstat at 3 degree of freedom =0.445

as p value is sginifiantly higher, hence we can not reject null hypothesis.Hence distribution of blood group is independent fo Rh factor.

Observed O O A B AB Total R+ 69 61 15 5 150 R- 44 39 9 8 100 Total 113 100 24 13 250 Expected E=rowtotal*column total/grand total O A B AB Total R+ 67.800 60.000 14.400 7.800 150 R- 45.200 40.000 9.600 5.200 100 Total 113 100 24 13 250 chi square =(O-E)^2/E O A B AB Total R+ 0.021 0.017 0.025 1.005 1.068 R- 0.032 0.025 0.038 1.508 1.602 Total 0.053 0.042 0.062 2.513 2.670

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