# Math Help - Adjusting a sample for population size

1. ## Adjusting a sample for population size

I have a sample of data for a number of cities in the UK that describes how commonly they are mentioned in the media (and I also have the associated city population size) :

City, Population, Mentions
Leeds,400000,434
London,7000000,30000
etc ...

I'd like to be able to compare the mentions on a like-for-like basis, adjusting so that city population size isn't a variable when comparing mentions.

I think the correct way to normalise the 'mentions' for each city is :

city_mentions * (1-(city_population/total_population_of_all_cities))

I'm unable to explain if this is correct though. I'd appreciate any alternate suggestions as to how this could/should be done or if the above method is correct.

Thanks

2. I would consider a hypothesis test for determining if there is a significant difference in proportions.

make $H_o: p_1 = p_2$

make $H_a: p_1 \neq p_2 \Rightarrow p_1 - p_2 \neq 0$