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Solution to question 6.1

The probability that we don't know the social class of a child in the fluoridated arm is simple to work out. There are 106 children in total and we don't know the class of 13 of them. So, the probability we don't know the social class (P) is:

P = 13÷106 = 0·12

Two decimal places would seem sufficient here. There certainly should be no more than three. You might have expressed this pobability as a percentage chance (of 12% or 12·3%)

The probability of a child in the defluoridated arm being in social class III is a bit more problematic. It is not really 53÷126, although this is the way I approached it in the lecture. in reality there is a problem caused by the not known category. These children will, in reality, belong to one of the other three categories (which we assume to be exhaustive). The best strategy to adopt here is probably to ignore the not known category and calculate the probability of being in social class III based on the adjusted total (126 - 19 = 107). So, the probability of being in social class III (P) is:

P = 53÷107 = 0·50

This is, strictly, only correct if the 19 children in the not known category are split between the three other categories in the same proportions to everyone else. This is probably not the case but we don't know. We have here an illustration of one of the problems resulting from inaccurate data collection.

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