Question

If other factors are held constant, what happens to a confidence interval if the sample variance increases? The range of t scores increases and the width of the interval increases. The range of t scores decreases and the width of the interval decreases. The standard error increases and the width of the interval increases. The standard error decreases and the width of the interval decreases.

Answer 1

The standard error increases and the width of the interval increases

Explanation:

The variance is equal to the square of the standard deviation. An increase in variance will increase the standard deviation.

The width of the confidence interval can be defined as:

`W=UL-LL=2z\sigma/√(n)`

The width is proportional to the standard deviation, so when the variance increases, the standard deviation and also the width of the interval increases.