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ELEN [110]
3 years ago
15

A recent survey based on a random sample of n=470 voters, predicted that independent candidate for the mayoral election will get

24% of the vote, but he actually got 27%. discuss whether the claim that suggest the survey was done incorrectly! explain your rational.
Mathematics
1 answer:
julsineya [31]3 years ago
7 0

I have an expression

\sigma = \sqrt{p(1-p)/n}

floating around in my head; let's see if it makes sense.

The variance of binary valued random variable b that comes up 1 with probability p (so has mean p) is

E( (b-p)^2 ) =  (-p)^2(1-p) + (1-p)^2p = p(1-p)

That's for an individual sample. For the observed average we divide by n, and for the standard deviation we take the square root:

\sigma = \sqrt{p(1-p)/n}

Plugging in the numbers,

\sigma = \sqrt{.24(1-.24)/490} = 0.019 = 1.9\%

One standard deviation of the average is almost 2% so a 27% outcome was 3/1.9 = 1.6 standard deviations from the mean, corresponding to a two sided probability of a bit bigger than 10% of happening by chance.

So this is borderline suspect; most surveys will include a two sigma margin of error, say plus or minus 4 percent here, and the results were within those bounds.

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