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Math Help - hypothesis test for mean less than number

  1. #1
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    hypothesis test for mean less than number

    a sample of 16 egg is take froom normal disribution. variance is unknown
    sample mean xbar is 4.49 and sample st dev, s, is 1.231
    you wish to do a test if the population mean is less than 5

    state h0 and h1, calculate test statistic and use the t disribution to find what level you can accept or reject h0.

    now i think the h0 is populationmean=5, h1 not equal 5?

    test statistic, t=(xbar-5)/(s/root of n)
    which i make =-1.657 please tell me if this right because if its wrong my lookup table will not even help..

    so now what i do with the t disribution table because i am confuse. i know degree of freedom is n-1 = 15. but i am confuse.
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  2. #2
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    1) If you are using H1: Mean <> 5, you have a 2-tailed test. That MAY be what you want and it may be the most appropriate place to start.
    2) You WILL need to select a level of significance. Remember to divide by 2 for a 2-tailed test.
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  3. #3
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    Quote Originally Posted by Caption12 View Post
    you wish to do a test if the population mean is less than 5
    H_0: \mu \geq 5

    H_1: \mu <5
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  4. #4
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    so it means is 1-tail

    my answer for t is negative but the t value table is positive

    now i am askin how do i read this answer of the t-table
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  5. #5
    Senior Member Sambit's Avatar
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    t distribution is symmetric about zero. If T is a random variable which follows t-distribution, then P(T<-t_{observed})=P(T>t_{observed}); so you can get the probability from a positive t-table.
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  6. #6
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    Show that the sample mean is an unbiased estimator of the population
    mean.
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