Question

Three things influence the margin of error in a confidence interval estimate of a population mean: sample size, variability in the population, and confidence level. For each of these quantities separately, explain briefly what happens to the margin of error as that quantity increases

Answer 1

If n be the sample size, s the standard deviation and z be the z score of required confidence level.

For margin of error E, E = Z•S/n^0.5 = Z•S•n^-0.5

(I) If n increases, clearly the margin of error decrease.

(ii) If variability increases, then variance and so standard deviation s increases. S and E are directly proportional, so when S increases then E increases.

(iii) If confidence level increases then its corresponding z value also increases, so E increases.