### Chapter 7, Survey Sampling

#### Solution 9

Let denotes the population in the sample.

Denoting as the member of population . Let if the member votes for the preposition and if the member votes against the preposition.

If denotes the proportion of the population that votes for the preposition and then denotes the proportion that votes against the preposition.

Thus the difference between and , i.e. , gives the estimated margin of victory in the sample population. The variance of this estimate is then .

We know that , ignoring the finite population correction.

Thus the variance of the estimated margin of victory is . And which gives the standard error = .

The 95% confidence interval is , or .

Or in percentage, The interval is .

Note: Compared to last problem here we used the approximation for , because population variance is not available.

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