Basic 2 problem -- Sickle-cell anemia is a hereditary condition that is more com
ID: 3222515 • Letter: B
Question
Basic 2 problem --
Sickle-cell anemia is a hereditary condition that is more common among blacks and can cause medical problems. A landmark study examined the relationship between sickle-cell anemia and malaria, a parasitic disease common in Africa. The study tested 543 African children for the sickle-cell gene and also for malaria. Here are the results:
heavy malaria infection
yes no
sickle-cell gene 36 100
no sickle-cell gene 152 255
Is there good evidence of a relationship between the sickle-cell gene and heavy malaria infection?
Use a 2 test:
State the null and alternative hypotheses for the 2 test.
Find the expected counts under the null hypothesis.
Use the expected counts to check the assumptions needed to use the 2 distribution to find the P value.
Calculate the test statistic from the observed and expected counts.
Explanation / Answer
Given table data is as below
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calculation formula for E table matrix
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expected frequecies calculated by applying E - table matrix formulae
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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above
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set up null vs alternative as
null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relationship between the sickle-cell gene and heavy malaria infection OR X and Y are dependent
level of significance, = 0.05
from standard normal table, chi square value at right tailed, ^2 /2 =3.8415
since our test is right tailed,reject Ho when ^2 o > 3.8415
we use test statistic ^2 o = (Oi-Ei)^2/Ei
from the table , ^2 o = 5.327
critical value
the value of |^2 | at los 0.05 with d.f (r-1)(c-1)= ( 2 -1 ) * ( 2 - 1 ) = 1 * 1 = 1 is 3.8415
we got | ^2| =5.327 & | ^2 | =3.8415
make decision
hence value of | ^2 o | > | ^2 | and here we reject Ho
^2 p_value =0.021
ANSWERS
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null, Ho: no relation b/w X and Y OR X and Y are independent
alternative, H1: exists a relation b/w X and Y OR X and Y are dependent
test statistic: 5.327
critical value: 3.8415
p-value:0.021
decision: reject Ho
we have evidence that relationship between the sickle-cell gene and heavy malaria infection
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