Question

If the accuracy of a sample average value is estimated using its standard error, then our original sample size is n=10, How much do you need to set n ' to double the accuracy?

Answer 1

To double the accuracy of a sample average by halving the standard error, the sample size must be quadrupled. Therefore, if the original sample size is n=10, the new sample size should be n=40.

Step-by-step explanation:

To double the accuracy of a sample average value estimated using its standard error, we need to adjust the original sample size. The standard error of the mean is inversely proportional to the square root of the sample size (n). Therefore, to double the accuracy, which is equivalent to halving the standard error, the sample size needs to be quadrupled. This is because when we square root the new sample size (n'), it should be double the square root of the original sample size (n). Hence, if n = 10, to double the accuracy, we need to set n' = 40.

Simply put, following the formula, since we are looking to double the accuracy (halve the standard error), we would solve the equation 2 * √n = √n'. Squaring both sides of this equation gives us 4n = n', which means that n' must be four times larger than the original n. As such, with n originally at 10, to achieve doubled accuracy, n' should be set to 40.