One week during an election campaign, three reputable polling firms used random

Question

One week during an election campaign, three reputable polling firms used random samples to estimate the percentage of voters supporting the Conservative party. The first firm reports an estimate of 29.8% with a standard error of 2.9%. The second firm reports an estimate of 26.2% with a standard error of 1.8%. The third firm reports an estimate of 31.1% with a standard error of 1.4%. [A] Combining this evidence, provide an estimate of the percentage of voters supporting the Conservatives. Report this percentage to one decimal place. [B] Give a standard error for your estimate in [A] (also to one decimal place).

Explanation / Answer

Solution:

We know here that, Mean =(A+B+C)/3

A) Estimate of the percentage of voters supporting the Conservatives= (29.8 + 26.2 + 31.3)/3 %

                                                                                                   = 29.1 %

B) Standard error = (1/3)*(SEA2 + SEB2 + SEC2 )1/2=(1/3)(2.92 +1.82 + 1.42)1/2 = 1.23

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