Results 1 to 2 of 2

Math Help - Random sample

  1. #1
    Member
    Joined
    Apr 2008
    Posts
    132

    Random sample

    A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.

    i) Obtain a 99% confidence interval for the true mean of the population
    ii) What would the interval be if the population variance were known to be
    σ^2 = 81?
    iii) If it is required to be 95% confident that the sample mean is to be correct to within 2 euro of the true mean ,what samle size is necessary? Use σ^2 = 81.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by matty888 View Post
    A simple random sample of size 10 drawn from a normal distribution yielded a sample mean of 100 and a sample variance of 64.

    i) Obtain a 99% confidence interval for the true mean of the population
    ii) What would the interval be if the population variance were known to be
    σ^2 = 81?
    iii) If it is required to be 95% confident that the sample mean is to be correct to within 2 euro of the true mean ,what samle size is necessary? Use σ^2 = 81.
    I'll assume that you're familiar with the notation I use.


    i) \left( \bar{x}-\frac{t_{\alpha/2} \, s}{\sqrt{n}}, ~ \bar{x} + \frac{t_{\alpha/2} \, s}{\sqrt{n}} \right)

    where t follows a t-distribution with n - 1 degrees of freedom and t_{\alpha/2} is the critical value of t. In your case n = 10 and \alpha = 0.01 \Rightarrow t_{0.005} = ........

    ---------------------------------------------------------------------------------------------

    ii) \left( \bar{x}-\frac{z_{\alpha/2} \, \sigma}{\sqrt{n}}, ~ \bar{x} + \frac{z_{\alpha/2} \, \sigma}{\sqrt{n}} \right)

    where z follows a standard normal distribution and z_{\alpha/2} is the critical value of z. In your case n = 10 and \alpha = 0.01 \Rightarrow z_{0.005} = ........

    ----------------------------------------------------------------------------------------------

    iii) Solve 2 = \frac{z_{\alpha/2} \, \sigma}{\sqrt{n}} for n, where \alpha = 0.05 \Rightarrow z_{0.025} = ........
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. A random sample X
    Posted in the Statistics Forum
    Replies: 4
    Last Post: January 1st 2010, 01:24 AM
  2. Random Sample from CDF
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 28th 2009, 09:55 AM
  3. Random sample
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 10th 2009, 02:23 AM
  4. Random Sample
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: August 2nd 2008, 04:57 AM
  5. Sample Random Sample Question 2
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: January 7th 2008, 06:58 AM

Search Tags


/mathhelpforum @mathhelpforum