LOS h: Explain the construction of confidence intervals.

A higher degree of confidence requires a wider confidence interval. The degree of confidence is equal to one minus the alpha level, and so the wider the confidence interval, the higher the degree of confidence and the lower the alpha level. Note that the lower alpha level requires a higher reliability factor which results in the wider confidence interval.

A higher degree of confidence (e.g. 99% instead of 95%) would require a higher reliability factor (2.575 instead of 1.96 assuming a normal distribution). A wider confidence interval corresponds to a lower alpha significance level and the point estimate does not affect the width of the confidence interval.

The confidence interval for a parameter is calculated as Point Estimate ± Reliability Factor × Standard Error. The reliability factor is based on the assumed distribution of the point estimate and the degree of confidence (1 ? a) for the confidence interval.