For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error b) increases as the margin of error increases
The sample size needed to guarantee a given margin of error is determined by the population standard deviation and the level of significance. The population standard deviation and the level of significance remain constant, so when the margin of error increases, the sample size must increase in order to keep the same level of accuracy. The increase in sample size is necessary because a larger margin of error requires more data to reach the same level of accuracy when compared to a smaller margin of error. For example, a margin of error of 5% requires a larger sample size than a margin of error of 1%. As the margin of error increases, the sample size must increase in order to maintain the same level of accuracy.
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