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Confidence interval/Hypothesis test for standard deviation

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    1) A random sample of 26 students who are enrolled in College A was taken and their SAT scores were recorded. The sample mean is 548 and the sample standard deviation is s=57. Assume population is normally distributed.

    a) Find a 98% confdience interval for the standard deviation of SAT scores of all the students who are enrolled in College A.

    b) The principal of College A claims that the standard deviation of SAT scores of studnets in her college is 48. Does the data support the principal's claim? Justify.


    2. Relevant equations
    Hypothesis testing/Confidence intervals


    3. The attempt at a solution
    I am OK with part a, but have some concerns about part b.

    For part b, is it a hypothesis testing (H_o: σ^2 = 48^2, H_a: σ^2 ≠ 48^2) problem or is it a confidence interval problem? Can it be answered solely by using confidence interval? I have seen a theorem saying that "reject H_o: μ=μ_o at the level alpha if and only if μ_o falls outside the 100(1-alpha)% confidence interval for μ", but that's just for μ. Does it also hold for μ1-μ2 and σ ???

    Thank you!
     
  2. jcsd
  3. Apr 26, 2009 #2
    So my key question here is: Does the similar relationship between confidence interval and hypothesis testing also hold for μ1-μ2 and σ ?
     
  4. Apr 27, 2009 #3
    Yes for two-tailed tests. If you look at the formulas, you can see the test statistic is just a rearrangement of the CI.

    For proportion p, the formulas are slightly different, but you can still use the CI method.

    One-tailed tests, as with μ, would need "one sided confidence intervals" or "confidence rays" whatever you want to call them.
     
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