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In a chemical process, the amount of a certain type of
Chapter , Problem 4.21(choose chapter or problem)
In a chemical process, the amount of a certain type of impurity in the output is difficult to control and is thus a random variable. Speculation is that the population mean amount of the impurity is 0.20 gram per gram of output. It is known that the standard deviation is 0.1 gram per gram. An experiment is conducted to gain more insight regarding the speculation that = 0.2. The process is run on a lab scale 50 times and the sample average x turns out to be 0.23 gram per gram. Comment on the speculation that the mean amount of impurity is 0.20 gram per gram. Make use of the Central Limit Theorem in your work.
Questions & Answers
QUESTION:
In a chemical process, the amount of a certain type of impurity in the output is difficult to control and is thus a random variable. Speculation is that the population mean amount of the impurity is 0.20 gram per gram of output. It is known that the standard deviation is 0.1 gram per gram. An experiment is conducted to gain more insight regarding the speculation that = 0.2. The process is run on a lab scale 50 times and the sample average x turns out to be 0.23 gram per gram. Comment on the speculation that the mean amount of impurity is 0.20 gram per gram. Make use of the Central Limit Theorem in your work.
ANSWER:Based on the Central Limit Theorem, the sample mean (x) is expected to be normally distributed around the true population mean (?) with a standard deviation equal to the standard error of the mean. In this case,