Chemistry 155 Introduction to Instrumental Analytical Chemistry

Chem 155 Unit 1 Page 17 of 313Confidence Interval (continued).If you know the standard deviation, σ, (less common case), then:The x% confidence interval for μ = x AVG ± zσ / N ½If you don’t know the standarddeviation, σ, (more commonly thecase), then:If you have only a roughestimate of x AVG , then you areless confident that it is close toμ, hence you divide by N ½ .The x% confidence interval for μ = x AVG ± ts / N ½In this case t is a function of NThis leaves only z and t – what are they? These numbers representthe multiple of one standard deviation (σ or s) that correspond to theconfidence interval. In the second case, s is only an estimate of σ, sothe error in s needs to be taken into account, so t is a function of the“number of degrees of freedom”. For our purposes, i.e. averagingmultiple identical measurements, the number of degrees of freedomis simply N-1.Page 17 of 313