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Why is my answer wrong? (statistics)

  1. Dec 10, 2012 #1
    Let [itex]\bar{X}[/itex] be the mean of a random sample of size n from a distribution that is [itex]N(\mu,9)[/itex]. Find n such that [itex]P(\bar{X}-1 < \mu < \bar{X}+1)=.90[/itex], approximately.

    My answer:

    [tex]-Z^* < \frac{\bar{X}-\mu}{9/\sqrt(n)} < Z^* [/tex] where [itex]-Z^*[/itex] and [itex]Z^*[/itex] are the critical values.

    So...

    For the confidence interval, we have [tex]\bar{x} \pm z^*(\frac{9}{\sqrt(n)})[/tex]

    When I looked up the normal table for [itex]z^*[/itex], I found that it was approximately equal to 1.29


    Since the question tells us that the confidence interval is [tex]\bar{X} \pm 1 [/tex], so I just solved [tex]1 = (1.29)(\frac{9}{\sqrt(n)})[/tex]...but my answer was wrong...it was supposed to be 24 or 25. Can anybody please help?

    Thanks in advance
     
    Last edited by a moderator: Dec 10, 2012
  2. jcsd
  3. Dec 10, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    A probability of 0.9 to be inside gives a probability of 0.05 for both sides. You have to look for 0.95 and not 0.90. In addition, this value should be at the other side of your =.
     
  4. Dec 10, 2012 #3

    Ray Vickson

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    Besides what 'mfb' has told you, there is always the issue of what the '9' means in N(μ,9). Most commonly, the notation is ## N(\mu, \sigma^2), ## so that ##\sigma = 3.## I have seen the other notation ##N(\mu,\sigma)## used occasionally, but it is rarer. You need to check the convention used by your textbook and/or course notes. (I won't spoil your fun by telling you the answer.)
     
    Last edited: Dec 11, 2012
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