By how many times does the sample size have to be increased to decrease the margin of error by a factor of one half 1 2?? The sample size must be increased by a factor of nothing to decrease the margin of error by a factor of one half 1 2. ?(Type a whole? number.) What is the general? relationship, if? any, between the sample size and the margin of? error? A. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of StartFraction 1 Over Upper M squared EndFraction 1 M2. B. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of StartFraction 1 Over Upper M EndFraction 1 M. C. Increasing the sample size by a factor M results in the margin of error decreasing by a factor of StartFraction 1 Over StartRoot Upper M EndRoot EndFraction 1 M. D. There is no relationship between the sample size and the margin of error.