Each of the 50 separate Local Authorities in a country collects data on the number of road accidents in a year (n) and the number of these in which a fatality occurred (f).Question 23In order to estimate the overall proportion (in the country) of road accidents in which a fatality occurred, which one of the following is best?Compute the ratio f/n for each Local Authority, sum these ratios and divide by 50Sum all the values of f to give a total F, sum all the values of n to give a total N and compute F/NSelect one Local Authority at random, all equally likely, and use its value of f/nAs in C, except that the chance of selecting any particular Local Authority should be proportional to its population
Question
Each of the 50 separate Local Authorities in a country collects data on the number of road accidents in a year (n) and the number of these in which a fatality occurred (f).Question 23In order to estimate the overall proportion (in the country) of road accidents in which a fatality occurred, which one of the following is best?Compute the ratio f/n for each Local Authority, sum these ratios and divide by 50Sum all the values of f to give a total F, sum all the values of n to give a total N and compute F/NSelect one Local Authority at random, all equally likely, and use its value of f/nAs in C, except that the chance of selecting any particular Local Authority should be proportional to its population
Solution
The best method to estimate the overall proportion of road accidents in which a fatality occurred in the country would be to sum all the values of f to give a total F, sum all the values of n to give a total N and compute F/N. This is because this method takes into account all the data from all the local authorities, providing a more accurate and representative estimate of the overall proportion. The other methods either only use data from one local authority, which may not be representative of the whole country, or average the ratios, which could skew the results if there are large differences in the number of accidents between local authorities.
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