Question

Name the 3 factors that influence margin of error for the mean of a continuous random variable and how each factor needs to change to lower it. One of the 3 factors actually does 2 things in reducing the margin of error, name both of those things.

Answer 1

standard deviation, sample size and confidence level are the three influencer for the margin of error

(A) To lower the margin of error, decrease the standard deviation because standard deviation is directly associated with margin of error

(B) To lower the margin of error, decrease the confidence level because confidence level is directly associated with margin of error as decrease in confidence level, decreases the critical value of z or t.

(C) To lower the margin of error, increase the sample size because sample size is inversely associated with margin of error. This means increase in sample size, decreases the margin of error and decrease in sample size, increases the margin of error.

Confidence level is the one thing which does 2 things in reducing the margin of error. First, it reduces the margin of error because the critical value decreases with decrease in confidence level. Second, it reduces the confidence interval width or length, when we decrease the confidence level.