You work for a pharmaceuticals company as a statistical process analyst. Your jo

Question

You work for a pharmaceuticals company as a statistical process analyst. Your job is to analyze processes and make sure statistical control. In one process, a machine is supposed to add 9.8 milligrams of a compound to a mixture in a vial. (Assume this process can be approximated by a normal distribution.) The acceptable range of amounts of the compound added milligrams 9.65 milligrams to 9.95 milligrams, inclusive. Because of an error with the release valve, the setting on the machine "shifts" from 9.8 milligrams. To check that the machine is adding the correct amount of the compound into the vials, you select at random three samples of five vials and find the mean amount of the compound added for each sample. A coworker asks why you take the 3 samples of size 5 and find the mean instead randomly choosing and measuring the amounts in 15 vials individually the machine's settings. Write a paragraph to your coworker explaining why you take 3 samples of size 5 and find the mean of each sample instead of randomly choosing and measuring the amounts in 15 vials individually to cheek the machine's setting.

Explanation / Answer

If we compair one large sample size and one small sample size ther clearly large sample size is batter because The standard error of the mean is calculated using two things,the standard deviation (sd) of the parent population (which we can't change),the sample size (which we can change) will be less but here there are three small samples of five compair with one large sample of 15. if we compair one small sample of five with one large sample of 15, clearly sample with 15 is batterbut if we compair results of all three samll samples,(because error is multplying and always in fraction, multplying will reduse it) standard error will be less if compair to one large sample.

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