Making comparisons with a reference value

Ruhng out crass and systematic errors, the titration values can vary only because of random errors. If so, the central limit theorem imphes that the average values of sets of titrations made on the same batch should follow Student s distribution. The average of the three titrations, 

To arrive at a conclusion about the vinegar, we need to decide if the evidence furnished by the three results is incompatible with the hypothesis that they came from a population with mean p = 4%. From Eq. (2.21) we have 

Substituting s = 0.2082%, that is, the standard deviation of the three titration results, and 2 = 4.303 (from Table A.2, with a 95% confidence level), we have 

Conclusion since the confidence interval contains the 4% reference value, we cannot affirm that this value is not the true value of the average for this batch of vinegar. (The speciahst would say we cannot reject the null hypothesis.) Even though the average of the three samples is below 

Adapted from Pearson, E. S. and Hartley, H. 0. Biometrika Tables for Statisticians, Vol. 1, 3 University Press, 1996. 

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