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Math Help - Need direction - Hypothesis Testing

  1. #1
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    Need direction - Hypothesis Testing

    I've worked through a set of practice questions and ran across this problem and don't see how I can solve it without \sigma. Can someone please give me some direction?

    Q: When someone dials 911 for an emergency, the average length of time to reach an operator is supposed to be no more than 30 seconds. However, in a recent survey of 81 such calls, the sample mean came out to be 32 seconds. Is the response time in fact too long? Use \alpha=.10

    So, \mu_0=30, n=81, and \bar{x}=32.
    H_o: \mu=30, and
    H_a: \mu>30.

    I wanted to use the Z or T test statistics but I guess I can't because I don't see that I'm provided with enough information to be able to use them.

    I really appreciate your help! I'm sure there is something basic that I'm not seeing.
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  2. #2
    MHF Contributor matheagle's Avatar
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    I would venture to guess that is a poisson rv and thus the variance is the same as the mean.
    (By the way I never sleep)
    If these are Poisson's then you have as n goes to infinity

    {\bar X-\mu\over \sigma/\sqrt{n}}\to N(0,1)

    but we can use the Law of Large Numbers and Slutsky's Theorem.
    There we have \sigma^2=\mu=\lambda

    So If this is a Poisson we can use either \bar X as estimate of \sigma^2
    or use the null hypothesis value as the estimate of the unknown variance.

    I'm making this guess since n is greater than 30 so I would guess they want to use the CLT.
    And if there isn't a sigma, we need to find a relationship between moo and sigma.

    Night Poisson Ivy
    Last edited by matheagle; March 2nd 2011 at 12:08 AM.
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  3. #3
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    Hi MathEagle!
    It also seemed to me that the problem may involve a Poisson RV. But how can I argue that when I'm not given any time intervals or such?

    Thanks! It's great to hear from you!

    -Poisson Ivy
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  4. #4
    MHF Contributor matheagle's Avatar
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    maybe they just left out sigma?
    so, how is Charms doing?
    are you in school?
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