Results 1 to 2 of 2

Math Help - Confidence Interval, unknown stand dev

  1. #1
    Member
    Joined
    Nov 2007
    Posts
    232

    Confidence Interval, unknown stand dev

    ...nvrm solved it myself....

    Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean, based on the following sample size n = 7: 1, 2, 3, 4, 5, 6, and 20. Change the number 20 to 7 and recalculate the confidence interval. Using these results, describe the effect of an outlier on the confidence interval.

    My attempt:

    n = 7

    1 - {\alpha} = .95

    \alpha = 0.05

    t_{\frac{\alpha}{2}} = t_0.025

    \mu = \frac{41}{7}

    S = \sqrt{\frac{1756}{7}} = 15.83847

    degrees of freedom = n - 1 = 7 - 1 = 6

    S_X = \frac{S}{\sqrt{n-1}}

    S_X = 6.466

    .95 CI = X \pm t_{\frac{\alpha}{2}} S_X

    .95 CI = (\frac{41}{7} \pm t_{0.025, 6} (6.466)

    .95 CI = (\frac{41}{7} \pm (2.447) (6.466)

    .95 CI = (\frac{41}{7} \pm (15.822)

    My answer for the first part of this question is wrong, I don't think I know how to properly take the standard deviation. Please check and correct.

    Answer for first part:
    -0.12 \leq \mu \leq 11.84
    Last edited by Macleef; November 1st 2009 at 05:05 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    I was right the first time. I wasn't sure what you meant by S and S_x....
    You left out the square root of n.

    the formula is \bar x \pm t_{n-1,\alpha/2}s/\sqrt{n}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: November 6th 2010, 11:47 PM
  2. Confidence Interval for unknown sigma
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 2nd 2009, 03:06 PM
  3. Confidence interval-population standard deviation unknown
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: April 4th 2008, 08:25 PM
  4. Replies: 1
    Last Post: April 4th 2008, 11:39 AM
  5. confidence unknown
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: December 31st 2007, 11:40 AM

Search Tags


/mathhelpforum @mathhelpforum