Question

Student Exercise 1      A Canadian longitudinal study1 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 the table below.

	Overweight	Not overweight	Total
Antibiotics	144	294
No antibiotics	37	141
Total

Calculate the proportions and express your answers as a decimal rounded to the nearest hundredth.
a. What is the proportion of all children in the study that were given
antibiotics during the first year of life?
b. What is the proportion of all children in the study that were classified as
overweight at age 9?
c. What is the proportion of those not receiving antibiotics that were
classified as overweight at age 9?
d. What is the proportion of all children classified as overweight that were
given antibiotics during the first year of life?

Answer 1

a) The proportion of all children in the study that were given antibiotics during the first year of life:
= Total children given antibiotics / Total children in the study

= (144 + 294) / 616

= 0.71

Therefore 0.71 is the required proportion here.

b) The proportion of all children in the study that were classified as overweight at age 9 is computed here as:

= Total overweight children / Total children

= (144 + 37) / 616

= 0.29

Therefore 0.29 is the required probability here.

c) The proportion of those not receiving antibiotics that were classified as overweight at age 9 is computed using Bayes theorem here as:
= Number of children who did not receive antibiotics that were classified as overweight / Total not receiving antibiotics

= 37 / (37 + 141)

= 0.21

Therefore 0.21 is the required proportion here.

d) The proportion of all children classified as overweight that were given antibiotics during the first year of life is computed here as:

= Number of overweight children that were given antibiotics / Total children classified as antibiotics

= 144 / (144 + 294)

= 0.33

Therefore 0.33 is the required probability here.