Which standard deviation to use.

In summary, the conversation discusses the use of standard deviation (SD) in testing hypotheses about the mean of a population. A client provided a sample of 800 observations with a sample SD of 0.21, and Quality Associates suggested using random samples of size 30 for ongoing monitoring. The question arises of which SD to use - the assumed population SD of 0.21 or the sample SD from the ongoing monitoring. The concept of measure in probability is also mentioned, which involves using a measure function to assign values to events or outcomes in a probability space.
  • #1
Sadiekhan
1
0
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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  • #2
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.
 
Last edited:
  • #3
concept of measure
 
  • #4
wat is statistics
 
  • #5
concept of measure in probability
 
  • #6
measure function in probability
 
  • #7
wat do u mean by measure in probability
 

1. What is standard deviation?

Standard deviation is a measure of how spread out a set of data points is from the average or mean. It measures the variability or dispersion of a dataset.

2. Why is standard deviation important?

Standard deviation is important because it allows us to understand the distribution of a dataset and how much the data points deviate from the mean. It is often used as a measure of uncertainty or risk in statistical analyses.

3. How do you calculate standard deviation?

To calculate standard deviation, you first need to find the mean of the dataset. Then, for each data point, subtract the mean and square the difference. Next, find the average of these squared differences. Finally, take the square root of the average to get the standard deviation.

4. What is the difference between population and sample standard deviation?

Population standard deviation is calculated using all the data points in a population, while sample standard deviation is calculated using a subset of the data points, known as a sample. Sample standard deviation is typically used when the entire population cannot be measured or when it is too large to be practical.

5. When should I use standard deviation?

Standard deviation is commonly used in scientific and statistical analyses to understand the variability of data and make comparisons between different datasets. It is especially useful in describing normally distributed data, where most of the data falls within one standard deviation of the mean.

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