If a person gives the right answer to a question of yes/no type concerning a certain fact, the answer is correct either because the person knows the truth or because he/she happens to guess the right response alternative. Suppose that such a question is given to the same persons on two occasions, and that between these occasions, a campaign is undertaken, the aim of which is to raise the level of knowledge in the population. A model is introduced for this situation, making it possible to estimate the proportion (PB) of persons who know the answer before the campaign, the difference (D=PA-PB) in knowledge after (PA) vs. before the campaign, and the rate (g) of persons who guess the correct answer without having the actual knowledge. Asymptoic variances for the estimates are also given. The method is illustrated by means of data from a socio-medical survey in Addis Ababa, were the spread of knowledge concerning various vaccinations was investigated.