申論題

2. The impurity level in a chemical used in laboratory experiments must not exceed 50 parts per million (ppm) in each batch. Each batch of the purchased chemical will be tested to see if the requirement is met using the hypothesis H₀:μ ≥50 vs. H₁:μ ＜ 50, where 4 is the mean impurity level, Suppose that 100 samples are tested from each batch, and the impurity measurements are normally distributed with mean u = 50 and standard deviation σ = 2 ppm. (Hint: Use - = -2.326 and the standard normal c.d.f.Φ(-2)= 0.0228)

(B) If the chance of accepting a batch of chemical that does not meet the standard is to be limited to no more than 1%, determine the critical value c so that H₀ can be rejected if ＜ c, where & is the mean impurity level of 100 samples. (6 marks)