Results 1 to 7 of 7

Math Help - 85% Confidence Intervals... Z-value?

  1. #1
    Newbie
    Joined
    Nov 2010
    Posts
    6

    85% Confidence Intervals... Z-value?

    I'm looking over corrections for one of my midterms and ran into a few problems giving me weird Z-values from confidence intervals that don't exactly correspond to my Cumulative T Distribution Table.

    Question
    A sample of 19 eggs of the Atlantic Fairy Tern are each measured. The mean diameter is 3.34 cm. The actual population standard deviation of the diameter is 0.2 cm, what is the lower limit of an 85% confidence interval on the mean?
    How do I calculate the Z value required? The answer it gives me is Za/2=1.44 but I have no clue why and can't find "Za/2" anywhere in my notes to determine how all of this works.

    Thanks!
    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
    29
    You Z-value looks fine, which you can use as the population standard deviation is known.

    You are after the lower bound so

    \displaystyle \bar{x}-Z_{\frac{\alpha}{2}}\times \frac{\sigma}{\sqrt{n}} = 3.34-Z_{\frac{0.15}{2}}\times \frac{0.2}{\sqrt{19}} = 3.34-1.4395\times \frac{0.2}{\sqrt{19}} =\dots

    Remember t\to z as n gets large
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2010
    Posts
    6
    Thanks, but I know it's right... I just don't know why.

    Where did the 1.44 (or 1.4395) come from? How would I find Z0.15/2 on a standard normal table? Or would I?
    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
    29
    Quote Originally Posted by QNev View Post
    Where did the 1.44 (or 1.4395) come from? How would I find Z0.15/2 on a standard normal table? Or would I?
    Thanks how I found it!

    This is a good one

    Z table - Normal Distribution

    Find area under the curve to be 0.85 and "between" this should illustrate why.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2010
    Posts
    6
    Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.
    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
    29
    Quote Originally Posted by QNev View Post
    Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.
    Most tables won't have these stange values, you can approximate between known values.

    Are you allowed to use a graphing calculator?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by QNev View Post
    Thanks for the link but that's no good on a final haha. I have tables with values for a tail with areas of .10, .05, .1, .05, .005, etc. but not some weird in-between values like .075 and .02 and stuff like that. I would love to find out a formula for these but I can't find it anywhere.
    You interpolate in the table you are given, if your table is for the cumulative standard normal you will want to look up the z-score for a tail probability of 0.075, which you get by interpolation between the values for tail probability 0.1 and 0.05.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Confidence Intervals...
    Posted in the Statistics Forum
    Replies: 1
    Last Post: April 22nd 2010, 12:41 AM
  2. confidence intervals
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: April 13th 2010, 09:31 AM
  3. Confidence Intervals
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: June 17th 2009, 06:28 AM
  4. Confidence Intervals
    Posted in the Statistics Forum
    Replies: 0
    Last Post: May 26th 2009, 08:53 AM
  5. Confidence Intervals
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: June 16th 2008, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum