Recall the breath analyzers described in Example 4.3.5. The following are thirty blood alcohol determinations made by Analyzer GTE-10, a three-year-old unit that may be in need of recalibration. All thirty measurements were made using a test sample on which a properly adjusted machine would give a reading of 12.6%.

(a) If μ denotes the true average reading that Analyzer GTE-10 would give for a person whose blood alcohol concentration is 12.6%, test H0: μ = 12.6 versus H1: μ = 12.6 at the α = 0.05 level of significance. Assume that σ = 0.4. Would you recommend that the machine be readjusted?
(b) What statistical assumptions are implicit in the hypothesis test done in part (a)? Is there any reason to suspect that those assumptions may not be satisfied?

12.3 12.7 13.6 12.7 12.9 12.6 12.6 13.1 12.6 13.1 12.7 12.5 13.2 12.8 12.4 12.6 12.4 12.4 13.1 12.9 13.3 12.6 12.6 12.7 13.1 12.4 12.4 13.1 12.4 12.9