A community-based study of respiratory illness during the first year of life was

Question

A community-based study of respiratory illness during the first year of life was conducted in North Carolina. As part of this study, a group of children were classified according to family socioeconomic status. The numbers of children in each group who experienced persistent respiratory symptoms are shown below Use these data to compute the probability of suffering from persistent respiratory symptoms in each socioeconomic group. Assume that the numbers are large enough to satisfy the frequentist definition of probability. Calculate the odds of experiencing persistent respiratory symptoms for both the middle and low socioeconomic groups relative to the high socioeconomic group. Does there appear to be an association between socioeconomic status and respiratory symptoms?

Explanation / Answer

a)      Probabilities

Low:- 31/79=0.3924

Middle:- 29/122=0.2377

High:- 27/192=0.1406

b)      Odds

Low:- 31:48

Middle:- 29:93

High:- 27:165

c)      

If we compute the correlation, we get the value to be -0.99. Hence, the association between the two is that as socio economic status goes up, the number of symptoms go down.

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