Question

Which of the following would increase the width of a confidence interval?

Changing from a 99% to 95% confidence level. Increasing the variability of the outcome. Increasing the sample size.
Removing an outlier from the data

Answer 1

The confidence interval for the mean can be written
\[\bar{x}-z\frac{\sigma}{\sqrt{n}}< \mu < \bar{x}+z\frac{\sigma}{\sqrt{n}}\]
where the value of z is 2.576 to find a 99% confidence level and 1.960 to find a 95% confidence level.
It can be seen that changing from a 99% to 95% confidence level would reduce the width of a confidence interval.
What would happen to the width of a confidence interval if the variability of the outcome increased thus increasing the standard deviation?

Answer 2

would increased. Thank you kropot

Answer 3

You're welcome :)