by what factor should the sample size in a poll be increased in order to cut the margin of error in half
To determine the factor by which a sample size in a poll should be increased in order to cut the margin of error in half, you need to understand the relationship between sample size, margin of error, and confidence level.
The margin of error is the range within which the true population parameter is estimated to be. It is influenced by the sample size and the desired level of confidence. A larger sample size generally results in a smaller margin of error, while a higher confidence level leads to a wider margin of error.
To cut the margin of error in half, we need to double the sample size (since a larger sample size reduces the margin of error). However, it's crucial to note that the margin of error decreases with the square root of the sample size. Therefore, to achieve a specific reduction in the margin of error, we need to increase the sample size by the square of that factor.
Let's say the original sample size is n, and you want to cut the margin of error in half. In this case, we need to increase the sample size by a factor of sqrt(2) ≈ 1.414. Calculating the sample size with the new margin of error involves multiplying the original sample size by the squared factor:
New sample size = n * (sqrt(2))^2 = n * 2
So, to cut the margin of error in half, you need to increase the original sample size by a factor of 2.