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 believed that when catalyst A is used, the population mean concentration exceeds 65%. The standard deviation is known to be σ= 5%. A sample of outputs from 30 independent experiments gives the average concentration of 

(a) Does this sample information with an average concentration of 

provide disturbing in-formation that perhaps μA 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 σ is still assumed to be 5% and X̅B turns outto be 70%. Comment on whether or not the sample information on catalyst B strongly suggests that μ_B is truly greater than μ_A. Support your answer by computing
(c) Under the condition thatμ_A = μ_B = 65%, give the approximate distribution of the following quantities (with mean and variance of each). Make use of the Central Limit Theorem.

i)

ii)

iii)

Transcribed Image Text:

TA = 64.5%. TA 64.5%