Question

Answer and explain. If all other quantities remain the same, what will happen to the width of a confidence interval if there is an increase in the:

1. confidence level;

2. sample size; and

3. standard deviation

Answer 1

General form of a confidence interval (CI):

A confidence interval estimates are intervals within which the parameter is expected to fall, with a certain degree of confidence.

The general form:

estimate ± critical value × std.dev of the estimate

or estimate ± margin of error

(a) An increase in the level of confindence , increases the confidence interval (because in this case critical value increases).

(b)An increase in the sample size , decreases the confidence interval (because in this case standard error decreases).

(c) An increase in the population standanard deviation , increases the confidence interval (because in this case standard error /deviation of estimate increases).