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Math Help - confidence intervals

  1. #1
    Junior Member
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    confidence intervals

    A random sample of size
    n = 21 is taken from a Normal distribution with unknown mean μ

    and known variance
    = 23.6. The sample mean is 1.3.

    (a) Write down the 100(1
    − a)% two–sided confidence interval for μ when a= 0.05.

    (b) If the length of the confidence interval is not exceed the value 2, what is the sample size that should be taken to ensure this?

    (c) Describe the changes to the confidence interval if variance
    is unknown and replaced by the

    sample variance.

    I struggle with part b), and part c)

    Any help would be great, thanks
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  2. #2
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    For part b) read this article. PEOD6/PD006: Determining Sample Size

    Quote Originally Posted by sj247 View Post
    (c) Describe the changes to the confidence interval if variance[/SIZE][/FONT][/SIZE][/FONT][FONT=CMR10][SIZE=3][FONT=CMR10][SIZE=3]is unknown and replaced by the[/LEFT]
    sample variance.


    Becomes \bar{x}\pm t_{df,\alpha}\times \frac{s}{\sqrt{n}}
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  3. #3
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    could you go through part b) in stages please. I've read the material but it hasnt helped.

    Thanks
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