1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confidence interval of mean

  1. Jul 26, 2017 #1
    1. The problem statement, all variables and given/known data
    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 ?

    2. Relevant equations


    3. The attempt at a solution
    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 ?
     

    Attached Files:

    • 672.jpg
      672.jpg
      File size:
      71.7 KB
      Views:
      17
    • 673.jpg
      673.jpg
      File size:
      43.4 KB
      Views:
      17
  2. jcsd
  3. Jul 26, 2017 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    If you know the value of σ from some theory or some larger external set of data, then use it. Otherwise, you have to use your sample data to estimate σ. That tends to give a slightly smaller estimate than it should for the general population, so a better estimate of σ is obtained by dividing by n-1 instead of n.
     
  4. Jul 26, 2017 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    I would say the second attachment is wrong: the correct distribution to use is the t-distribution with ##n-1## degrees of freedom. However, for large ##n## there is not much difference between the t-distribution and the normal distribution, so it is a reasonable approximation to replace the t by the normal. For example, when ##n=31## (30 degrees of freedom) we have
    $$
    \begin{array}{cc}
    P(N \leq -1) = 0.15866, & P(T \leq -1) = 0.16265\\
    P(N \leq 1) = 0.84134, & P(T \leq 1) = 0.83735
    \end{array}
    $$
     
  5. Jul 28, 2017 #4
    Do you mean that for large sample size n > 30 , it's okay to use the assumption that the standard deviation of the population equal to the standard deviation of the sample ?
     
  6. Jul 28, 2017 #5
    Do you mean that for large sample size n > 30 , it's okay to use the assumption that the standard deviation of the population equal to the standard deviation of the sample ?
     
  7. Jul 28, 2017 #6

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    For any size sample, if you don't have some other way of knowing the value of σ, then you have no alternative to using the sample standard deviation.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Confidence interval of mean
  1. Confidence Interval (Replies: 3)

  2. Confidence Intervals (Replies: 1)

  3. Confidence Intervals (Replies: 5)

Loading...