The concentration of an active ingredient in the output of a chemical reaction is strongly influenced by the catalyst that is used in the reaction. It is felt that when catalyst A is used the population means concentration exceeds 65%. The standard deviation is known to be a = 5%. A sample of outputs from 30 independent experiments gives the average concentration of x_A = 64.5%.

(a) Does this sample information with an average concentration of x_A = 64.5% provide disturbing information that perhaps μ_A is not 65%, but less than 65%? Support your answer with a probability statement.

(b) Suppose a similar experiment is done with the use of another catalyst, catalyst B. The standard deviation a is still assumed to be 5% and x_B turns out to be 70%. Comment on whether or not the sample information on catalyst B seems to give strong information that suggests that μ_B is truly greater than μ_A. Support your answer by computing P(X_B – X_A > 5.5 | μ_B = μ_A).

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i)XB: ii)XA - XB; iii) Sa-&n 1/30