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)

(C) If the measurements from one batch of the chemical had a sample mean of = 49.6 ppm of impurities, will H₀ be rejected using a = 0.05? Also, write down the definition of the P-value and calculate it. (15 marks)