Question

An investigation is conducted to determine if the exposure of women to atomic fallout influences the rate of birth defects. A sample of 500 children born to mothers who were exposed to the atomic explosion in Hiroshima was studied. A sample of 400 children from a Japanese island far removed from the site of the atomic explosion formed the control group. Suppose that the following data and R output for the incidence of birth defects were obtained. Expected counts are printed below observed counts.

Present Absent Total

exposed 84 416 500

70.56 A

not exposed 43 357 400

56.44 343.56

total 127 773 900

χ2=2.562 + B + 3.202 + 0.526 = C

[a] Provide calculations of A, B and C.

[b] Is this a test of independence or a test of homogeneity? Explain.

[c] Do these data indicate that there is a different rate of incidence of birth defects for

the two groups of mothers? Provide hypotheses of interest, p-value calculations, and a conclusion.

Answer 1

	Observed Frequencies
	0
0	present	absent					Total
exposed	84	416					500
not exposed	43	357					400
Total	127	773					900

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	present	absent					Total
exposed	127*500/900=70.56	773*500/900=429.44					500
not exposed	127*400/900=56.44	773*400/900=343.56					400
Total	127	773					900

	(fo-fe)^2/fe
exposed	2.562	0.421
not exposed	3.202	0.526

a)

A =  429.44

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   6.711

χ2=2.562 + B + 3.202 + 0.526 = C

C = 6.711

B = 0.947

b)

Test of independence

As we are using chi test of independence

c)

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   6.711

Ho: given two variable are independent
H1: Given two variables are not independent

Level of Significance =   0.1
Number of Rows =   2
Number of Columns =   2
Degrees of Freedom=(#row - 1)(#column -1) = (2- 1 ) * ( 2- 1 ) =   1
  
p-Value =   0.0096
Decision:    p-value < α , Reject Ho

There is sufficient evidence to support that the exposure of women to atomic fallout influences the rate of birth defects.

Please revert in case of any doubt.

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