Chemistry 155 Introduction to Instrumental Analytical Chemistry

Chem 155 Unit 1 Page 22 of 3131.5.6 t EXP PROBLEM:Another way of approaching this type of problem is to calculate anexperimental value of ‘t’ called t EXP.In the example below, we will compare a measured result with anexact one. The question one answers with t EXP is this: Am I confidentthat the observed value (x) differs from the expected value (μ)?Our threshold temperature, exactly 102° was tested, so we can makemeasurements and test the hypothesis that ‘the true temperature isgreater than 102°’.Given the following three measurements of a passenger’stemperature: 103.76°, 102.11°, 105.38° – calculate an experimentalvalue of the ‘t’ statistic for this population relative to the true value of102°. Average = 103.75, std dev = 1.34% confidence interval°freedom 50 80 95 991 1.00 3.08 12.71 63.662 0.82 1.89 4.30 9.923 0.76 1.64 3.18 5.84( x av − μ) ⋅ Nt expsμ = test value( 103.76−102) ⋅ 3t exp :=1.34t exp = 2.275Can you state with the given confidence that this person’stemperature differs from the expected value of 102°?99%? No95%? No80%? Yes50%? YesPage 22 of 313