Results 1 to 8 of 8
Like Tree1Thanks
  • 1 Post By pickslides

Math Help - Finding the confidence interval from a sample of a normal population

  1. #1
    Member
    Joined
    Sep 2009
    Posts
    104
    Thanks
    1

    Finding the confidence interval from a sample of a normal population

    Hey everyone! I'm having difficulty figuring out this question. It seems simple and straightforward enough, but I need some guidance as to what I need to do.
    Consider the sample 49 53 49 47 52 61 50 49 from a normal population with population mean μ and population variance σ2. Find the 95% confidence interval for μ
    I know the x̄=51.25 and s = 4.367 and n = 8 but I don't understand how to find the confidence interval from this point on..

    The formula I'm given is:

    x̄ za/2 * (s/√n)

    I know x̄ and s are, and I know a/2 = 0.05/2, the z-score that lines up with (0.5-[0.05/2]) is 1.96, but I don't know n, so how would I solve this?

    any help appreciated!

    EDIT: I also know that x̄ is representative of μ.

    The answer key says the answer is 51.25 3.65, but I don't understand where 3.65 came from.
    Last edited by snypeshow; March 19th 2012 at 05:45 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Finding the confidence interval from a sample of a normal population

    Quote Originally Posted by snypeshow View Post


    The answer key says the answer is 51.25 3.65, but I don't understand where 3.65 came from.
    Try 1.96 \times \frac{4.367}{\sqrt{8}}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    104
    Thanks
    1

    Re: Finding the confidence interval from a sample of a normal population

    that equals 3.026, the answer was 3.65
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Finding the confidence interval from a sample of a normal population

    The answer key is sometimes wrong.


    If this is for submission show your workings, this will show your assessor you have an understanding of the topic.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2009
    Posts
    104
    Thanks
    1

    Re: Finding the confidence interval from a sample of a normal population

    I thought that too, so i decided to apply what you said to the next 4 exercises, and they're wrong as well. So then I'm guessing the way I calculated za/2 is wrong, but I don't know any other possible logical way to get that number..
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Finding the confidence interval from a sample of a normal population

    Igniore my previous comments.

    Now as \sigma is not known and n is small, discard Z_{\frac{\alpha}{2}} in favour of t_{n-1,\frac{\alpha}{2}}
    Last edited by pickslides; March 19th 2012 at 06:51 PM.
    Thanks from snypeshow
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Sep 2009
    Posts
    104
    Thanks
    1

    Re: Finding the confidence interval from a sample of a normal population

    Awesome! Thanks a lot!

    How exactly would you know if n is small or big? in this case, n = 8 but 8 being "small" or "big" is relative in terms of another number (i.e. 8 is bigger than 7, but 8 is smaller than 20). Is there a set rule as to how big n should be?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Master Of Puppets
    pickslides's Avatar
    Joined
    Sep 2008
    From
    Melbourne
    Posts
    5,236
    Thanks
    28

    Re: Finding the confidence interval from a sample of a normal population

    Rule of thumb, n=30 is large enough as data distribution can be observed by then.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Confidence Interval for population mean
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: June 5th 2010, 03:02 AM
  2. Confidence Interval for Population Standard Deviation
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 20th 2009, 08:47 AM
  3. large sample, confidence interval
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 24th 2009, 03:26 PM
  4. Replies: 2
    Last Post: January 29th 2009, 07:23 AM
  5. Sample Size & Confidence Interval
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 9th 2007, 08:04 AM

Search Tags


/mathhelpforum @mathhelpforum