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Math Help - Confidence intervals, hypothesis testing etc.

  1. #1
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    Unhappy Confidence intervals, hypothesis testing etc.

    Here r some Statistics Questions. Can someone help me to answer them?

    1. Suppose a sample of n = 25 items is drawn from a population described
    by a Normal distribution with standard deviation σ = 16, and that the
    sample mean of the 25 values is 96.4. Derive a 95% confidence interval
    for μ, the (unknown) mean of this distribution, and use your confidence
    interval to test, at the 5% significance level, the hypothesis H0 : μ = 100
    against the general (two-sided) alternative H1 : μ = 100.

    2. Outline the changes to all calculations in Q1 if, instead of knowing
    σ = 16, we have to estimate this quantity from the sample data, and
    our estimate is
    s = 17.
    Repeat the test of the hypothesis in Q1, and decide whether your conclusions
    change in these circumstances.

    3. Illustrate the p-values for the above hypothesis (with σ known or not),
    using sketches based on the appropriate reference distribution. Calculate
    the p-values associated with the tests outlined in Q1 and Q2.
    Last edited by mr fantastic; May 9th 2010 at 03:10 AM. Reason: Re-titled.
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