Which standard deviation to use.

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In the discussion about which standard deviation to use for hypothesis testing, it is clarified that the population standard deviation can be assumed to be 0.21 based on the large initial sample of 800 observations. However, when monitoring the process with smaller samples of size 30, the sample standard deviation should be used instead, particularly if the goal is to detect changes in the population. The assumption of the population standard deviation being valid relies on the process operating satisfactorily during the initial sampling. For samples of 30 or more, utilizing the sample standard deviation along with Z scores is recommended for estimating confidence intervals. This approach ensures accurate monitoring of the process over time.
Sadiekhan
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I have a question of testing of hypothesis about mean, the population S/d is not given rather it says
"a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was .21; hence, with so much data, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis."

Now I am confused as to which s.d to use, do I have to use 0.21 as standard deviation
(considering it the population s.d ) or do I have to use the s.d of the size 30 sample?

Thanks In advance.
 
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Sadiekhan said:
"a client gave Quality Associates a sample of 800 observations taken during a time in which that client’s process was operating satisfactorily. The sample standard deviation for these data was .21; hence, with so much data, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis."

Now I am confused as to which s.d to use, do I have to use 0.21 as standard deviation
(considering it the population s.d ) or do I have to use the s.d of the size 30 sample?

Thanks In advance.

Given that the process was sampled when it was running satisfactorily, you would have to be able to carry this assumption forward in order to assume the earlier estimate of the population SD is good enough to take it as the population SD.

I would assume you don't know the population SD since you are monitoring for changes in the population. However, if your samples are 30 or more, you can use the sample sd and Z score to estimate the confidence intervals from the samples taken during monitoring.
 
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