Which standard deviation to use.

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Discussion Overview

The discussion revolves around the appropriate standard deviation to use when testing hypotheses about the mean, particularly in the context of monitoring a process based on sample data. Participants explore the implications of using a sample standard deviation versus an assumed population standard deviation derived from a larger sample.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether to use the assumed population standard deviation of 0.21 or the standard deviation from smaller samples of size 30 for ongoing monitoring.
  • Another participant suggests that the assumption of the population standard deviation being 0.21 can only be carried forward if the process remains stable and satisfactory.
  • It is noted that if the samples are of size 30 or more, the sample standard deviation can be used along with the Z score to estimate confidence intervals during monitoring.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the appropriate standard deviation to use, indicating that multiple competing views remain on this topic.

Contextual Notes

There is a lack of consensus on whether the population standard deviation can be reliably assumed based on the initial sample, and the implications of monitoring changes in the population are not fully resolved.

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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concept of measure
 
wat is statistics
 
concept of measure in probability
 
measure function in probability
 
wat do u mean by measure in probability
 

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