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Answer

The margin of error is proportional to 1/, where n is the sample size. So to reduce the margin of error by a factor of 3, we need to increase the sample size by a factor of 9. (If n becomes 9 times bigger, the margin of error becomes = 3 times smaller.) Hence to achieve a margin of error of 1 percentage point, we would need to increase the sample size from 1000 to 9000.

This example shows why decreasing the sampling error beyond a certain point quickly becomes impractical. It is quite likely that sampling 9000 people for a political poll would be prohibitively expensive. Furthermore, there may be unavoidable biases in the sampling techniques (as discussed in the previous section), which introduce additional sources of error in the estimate. Increasing the sample size does nothing to reduce these errors.

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