The question relates to the concept of standard error in the context of statistics, which is a part of mathematics. Specifically, it addresses the effect of increasing the sample size on the precision of sample estimates, such as the sample proportion. The standard error of the sample proportion is inversely proportional to the square root of the sample size. Therefore, if you increase the sample size by a factor of four (n x 4), the standard error is reduced by a factor of two (1/√4), which is one-half. This relationship is key for designing experiments and interpreting statistical data.
Moreover, the confidence interval for a sample proportion can be adjusted for more accuracy by using the plus-four method, which effectively increases the sample size (n + 4) and the number of successes (x + 2). Computer studies support the usage of the plus-four method for enhancing the estimation of the standard deviation of the sampling distribution, particularly when the desired confidence level is 90 percent or higher and the sample size is at least ten.
Final answer is Increasing the sample size by a factor of four reduces the standard error by a factor of one-half. This is because the standard error is inversely related to the square root of the sample size. The plus-four confidence interval method improves the estimation of the standard deviation and standard error.