Standard deviation help needed

J

jimi

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Feb 1, 2005
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Hi all,
This is a question from a UK GCSE Statistics paper (June 2024)

'Faiza owns a factory that makes footballs. The production line is set up to make footballs with a diameter of 219 mm.
As a quality control check, random samples are taken and the mean diameter of each sample is calculated.
The sample means should be normally distributed with a mean of 219 mm and a standard deviation of 0.05 mm.

(a) Would the sample means or the population values be more consistent? Give a reason for your answer.'

We are told that the sample standard deviation is 0.05 mm but we are not told what the population standard deviation is. Therefore, I fail to see how we can answer this question. What am I missing?
 
jimi said:
We are told that the sample standard deviation is 0.05 mm but we are not told what the population standard deviation is.
Click to expand...
We also aren't told how big the samples are.

But we can still think about whether the standard deviation of sample means will be greater or less than the standard deviation of the population. If you did know the sample size and the population standard deviation, how would you find the expected distribution of sample means?
 
Dr.Peterson said:
We also aren't told how big the samples are.

But we can still think about whether the standard deviation of sample means will be greater or less than the standard deviation of the population. If you did know the sample size and the population standard deviation, how would you find the expected distribution of sample means?
Click to expand...
Thank you for replying.
I think I understand what you're getting at. Are we to assume that the population is normally distributed? If so, the sample standard deviation would be the population standard deviation divided by the square root of sample size. Therefore, the sample standard deviation would be smaller and therefore sample means would be more consistent. Is that right?
 
Yes, that's what I have in mind, and perhaps it is what the authors are thinking.
 
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