Question

Increasing the sample size while keeping the same confidence level has what effect on the margin of error? A. Increases the margin of error and hence increases the precision B. Increases the margin of error and hence decreases the precision C. Decreases the margin of error and hence increases the precision D. Decreases the margin of error and hence decreases the precision E. None of the above

Answer 1

Answer:

C. Decreases the margin of error and hence increases the precision

Step-by-step explanation:

If we select a sample by Simple Random Sampling in a population of “infinite” size (a population so large that we do not know its size exactly), then the margin of error is given by

$\bf E=\frac{ZS}{\sqrt{n}}$

where  

Z = The Z-score corresponding to the confidence level

S = The estimated standard deviation of the population

n = the size of the sample.

As we can see, since n is in the denominator of the fraction and the numerator is kept constant, the larger the sample size the smaller the margin of error, so the correct choice is:

C. Decreases the margin of error and hence increases the precision