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 mean concentration exceeds 67%. The standard deviation is known to be o = 5%. A sample of outputs from 30 independent experiments gives the average concentration of XA = 66.5%. a. Does this sample information with an average concentration of X4 = 66.5% provide disturbing information that perhaps µ is not 67%, but less than 67%? Support your answer with a probability statement. What is that probability? b. Suppose a similar experiment is done with the use of another catalyst, catalyst B. The standard deviation is still assumed to be 5% and XB turns out to be 72%. Comment on whether or not the sample information on catalyst B strongly suggest that µg is truly greater than Ha. Support your answer by computing P(XB - XA 2 5.5| HB = HA Place your comments/interpretations in your solution file/s.

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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 mean concentration exceeds 67%.
The standard deviation is known to be o = 5%. A sample of outputs from 30
independent experiments gives the average concentration of XA = 66.5%.
a. Does this sample information with an average concentration of XA = 66.5%
provide disturbing information that perhaps µ is not 67%, but less than 67%?
Support your answer with a probability statement. What is that probability?
b. Suppose a similar experiment is done with the use of another catalyst, catalyst B.
The standard deviation is still assumed to be 5% and XB turns out to be 72%.
Comment on whether or not the sample information on catalyst B strongly
suggest that ug is truly greater than Ha. Support your answer by computing
P(XB - XA 2 5.5 | µB = HA)-|
Place your comments/interpretations in your solution file/s.
Transcribed Image Text: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 mean concentration exceeds 67%. The standard deviation is known to be o = 5%. A sample of outputs from 30 independent experiments gives the average concentration of XA = 66.5%. a. Does this sample information with an average concentration of XA = 66.5% provide disturbing information that perhaps µ is not 67%, but less than 67%? Support your answer with a probability statement. What is that probability? b. Suppose a similar experiment is done with the use of another catalyst, catalyst B. The standard deviation is still assumed to be 5% and XB turns out to be 72%. Comment on whether or not the sample information on catalyst B strongly suggest that ug is truly greater than Ha. Support your answer by computing P(XB - XA 2 5.5 | µB = HA)-| Place your comments/interpretations in your solution file/s.
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