Chapter 6.2, Problem 7Q

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 $\mu$ denotes the true average reading that Analyzer GTE-10 would give for a person whose blood alcohol concentration is 12.6%, test

  $H_0:\mu =12.6$

  Versus

  $H_1:\mu \ne 12.6$

  at the $\alpha =0.05$ level of significance. Assume that $\sigma =0.4$. 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?