The United Kingdom\'s population of 64 million people is distributed as 83.9% in

Question

The United Kingdom's population of 64 million people is distributed as 83.9% in England, 8.4% in Scotland, 4.8% in Wales, and 2.9% in Northern Island Separate random samples of size 500 were conducted in each of the four countries. The number of respondents supporting European Union membership were 268 in the English sample, 311 in the Scottish sample, 225 in the Welsh sample, and 253 in the Northern lrish sample. [A] Using these data, give an estimate of the proportion of United Kingdom residents who support European Union membership (report your estimated proportion to three decimal places). [B] Give a standard error to accompany your estimate in part [A] (also to three decimal places).

Explanation / Answer

P(English supporting EU membership) = 268/500 = 0.536

P(Scottish supporting EU membership) = 311/500 = 0.622

P(Welsh supporting EU membership) = 225/500 = 0.45

P(Northern Irish supporting EU membership) = 253/500 = 0.506

A ] proportion = 0.839*0.536+0.084*0.622+0.048*0.45+0.029*0.506 = 0.538

B] 0.022

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