summary a confidence interval for the population mean, is constructed using the formula: sample mean...

Summary

A confidence interval for the population mean, is constructed using the formula:

sample mean ± z multiplied by σ/√nwhere σ is the population standard deviation, n is the sample sizeand z is dependent on the confidence level.Eg z = 1.96 for a confidence level of 95%

June 06 q4

June 07 q3

The meaning of a confidence interval

It is important that you understand what is meant by a confidence interval. For example, if you find a 90% confidence interval, this does NOT mean that there is a 90% chance that the mean lies within the confidence interval. It means that if you take many samples of the same size and construct a 90% confidence interval from each one, then 90% of these intervals will contain the true population mean.

This may seem like a subtle distinction, or just a different wording. The important point, however, is that the true population mean is not random. Even though you don’t know what it is, it is fixed. Either a particular confidence interval contains the mean, or it doesn’t. So you cannot say that there is a 90% chance that a particular confidence interval contains the mean.

However, the confidence interval is a random variable as it is based on a random sample. So you can say that 90% of intervals calculated from samples of a given size will contain the true mean.