Confidence intervals are used to estimate a range within which a population parameter is likely to lie. Confidence intervals can be calculated for pretty much any population parameter, but they are most frequently used to estimate population means and proportions. The video demonstrates a spreadsheet model for estimating a population mean from a random sample.
It should be noted that it is much more common that the standard deviation is not known. For completeness I will demonstrate both methodologies and point out the difference between them.
Of course we would like to be 100% sure that our interval contains the population mean, however almost nothing is certain and since we are using properties of the normal distribution to calculate our interval – a distribution that is not closed - we can’t be 100% certain. So we have to settle for “pretty certain”. In general pretty certain is somewhere around 90% or 95%, and we will see that there is a trade off for being more certain. The difference between our chosen certainty or confidence level and 100% is called alpha and it is also the probability that the interval we end up with does not contain the population mean. Alpha is also referred to as the level of significance.
The spreadsheet used in this video may be downloaded from: Our resources page