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notes 29

# notes 29 - Constructing confidence intervals to estimate a...

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Constructing confidence intervals to estimate a population mean Submitted by gfj100 on Wed, 11/11/2009 - 12:50 Previously we considered confidence intervals for 1-proportion and our multiplier in our interval used a z-value. But what if our variable of interest is a quantitative variable (e.g. GPA, Age, Height) and we want to estimate the population mean? In such a situation proportion confidence intervals are not appropriate since our interest is in a mean amount and not a proportion. Therefore we apply similar techniques but now we are interested in estimating the population mean, μ, by using the sample statistic and the multiplier is a t-value. These t-values come from a t-distribution which is similar to the standard normal distribution from which the z-values came. The similarities are that the distribution is symmetrical and centered on 0. The difference is that when using a t-table we need to consider a new feature: degrees of freedom ( df ). This degree of freedom will be based on the sample size, n. Initially we will consider confidence intervals for means of two situations:

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