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Thread: Confidence interval of mean

  1. #1
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    Confidence interval of mean

    Both images are 2 consecutive pages of my notes . In this theory , i was told to use z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) . However , in the 2nd image , i was told to replace σ with s ( sample standard deviation) . Which is correct ?


    I think the first theory of using z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) is correct , and the replace σ with s ( sample standard deviation) . is wrong . Am i right ?

    Confidence interval of mean-672.jpgConfidence interval of mean-673.jpg
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  2. #2
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    Re: Confidence interval of mean

    Quote Originally Posted by xl5899 View Post
    Both images are 2 consecutive pages of my notes . In this theory , i was told to use z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) . However , in the 2nd image , i was told to replace σ with s ( sample standard deviation) . Which is correct ?


    I think the first theory of using z-distribution when the sample size is large ( more than 30) and the standard deviation of the population , σ is known) is correct , and the replace σ with s ( sample standard deviation) . is wrong . Am i right ?

    Click image for larger version. 

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ID:	37906Click image for larger version. 

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    It is always better to use \sigma instead of s; however, in practice you will often be given a large set of data and will only be able to compute s. When your data are large enough, you may approximate \sigma with s.

    Bottom line: Use \sigma if you have it, but don't hesitate to use s if your data are large as an approximation to \sigma.

    I hope this clears things up for you.
    Best,
    Andy
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  3. #3
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    Re: Confidence interval of mean

    Quote Originally Posted by abender View Post
    It is always better to use \sigma instead of s; however, in practice you will often be given a large set of data and will only be able to compute s. When your data are large enough, you may approximate \sigma with s.

    Bottom line: Use \sigma if you have it, but don't hesitate to use s if your data are large as an approximation to \sigma.

    I hope this clears things up for you.
    Best,
    Andy
    Let me add one more bit to this. The Z-test assumes the standard deviation(s) is(are) known.
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