Question

What happens to the width of a confidence interval for a population mean if the level of confidence is increased without changing the sample size? Assume that the population standard deviation is unknown and the population distribution is approximately normal. Select your answer from the choices below.

Answer 1

The increase in the level of confidence means that the interval will be wider.

Explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

`M = z(s)/(√(n))`

In which z is related to the confidence level(if the confidence level increases z increases), s is related to the standard deviation and n is the sample size.

The higher the margin of error, the wider the interval is.

In this question:

Increasing the level of confidence will mean an increase in z, and thus, since M and z are directly proportional, the margin of error will increase, and the inteval will be wider.