9. According to an article in a recently published medical journal, one-third of

Question

9. According to an article in a recently published medical journal, one-third of all sets of triplets consist of all females, one-fourth are all male sets, and the remaining sets are of mixed gender. A simple random sample of 78 sets of triplets born in the past 20 years is obtained from hospital records. The results are presented below. Gender make-up of triplets 1: All female 2: All male 10 3: Mixed gender 57 Total 78 Under the null hypothesis that the claim made in the medical journal is indeed true, what is the contribution to the chi-square statistic from each of the three cells?

Explanation / Answer

null hypothesis:Ho: proportion of triplets follow distribution as per medical Journal

alternate hypotheis: Ha: proportion of triplets differs from distribution as per medical Journal

applying chi square goodness of fit test:

hence contribution to chi square test statistic from all female =9.85

contribution to chi square test statistic from all male =3.71

contribution to chi square test statistic from mixed gender =18.47

observed Expected Chi square x Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei all female 1/3 10.000 26.0 9.85 all male 1/4 11.000 19.5 3.71 mixed gender 5/12 57.000 32.5 18.47 total 1 78 78 32.021

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