A Canadian longitudinal study examines whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The children were classified as having received antibiotics or not during the first year of life and then being overweight or not at 9 years old. The study included 616 children, and the results are shown in Table 2.14.

(a) What proportion of all children in the study were given antibiotics during the first year of life? 

(b) What proportion of all children in the study were classified as overweight at age 9? 

(c) What proportion of those receiving antibiotics were classified as overweight at age 9? 

(d) What proportion of those not receiving antibiotics were classified as overweight at age 9? 

(e) If we use p̂_A to denote the proportion from part (c) and p̂_N to denote the proportion from part (d), calculate the difference in proportion being overweight, p̂_A − p̂_N, between those who were exposed to antibiotics and those who weren’t. 

(f) What proportion of all children classified as overweight were given antibiotics during the first year of life?

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Table 2.14 Does antibiotic exposure early in life affect weight later in life? Antibiotics No antibiotics Total Overweight 144 37 181 Not overweight 294 141 435 Total 438 178 616