Question

Which of the following is a benefit of increasing the sample size when trying to estimate the mean from a sample average?

a. A reduction in the bias of the estimate.
b. A reduction in the variability of the estimate.
c. An increase in the width of the resulting confidence interval.
d. There will be no benefit because the population has not changed.

Answer 1

Explanation:

The larger the sample size, the lower the standard deviation. The standard deviation shows how the data is spread from the mean. Therefore, benefit of increasing the sample size when trying to estimate the mean from a sample average are

a. A reduction in the bias of the estimate.

b. A reduction in the variability of the estimate.

The width of confidence interval is determined by the margin of error

Margin of error = z × s/√n

A smaller standard deviation and increased size would result to a narrower confidence interval. Therefore, increasing the sample size does not result to an increase in the width of the resulting confidence interval.