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  • Maths gurus Quiz
  • duntstick
    Free Member

    I told my boffin daughter that STW has all the answers, can anyone help me win the internetz? 🙂

    An excavation of an early Upper Paleolithic cave site in France gave two samples of hominid skeletons: a sample of Homo Sapiens Sapiens (n1 = 20) and a sample of Homo Sapiens Neandertalis (n2 = 20).
    We are interested in establishing whether there is any significant difference between the cranial capacities of these two hominid species from this cave site.
    Let X1 = 1514.6 the sample mean of cranial capacities (cm3) for the Homo Sapiens Sapiens specimens, and X2 = 1553.4 for the Homo Sapiens Neadnertalis.
    Also, the sample standard deviation is s1 = 78.4 for the first and .s2 = 74.7 for the second group, respectively.

    Q.
    If one rejected the null hypothesis when the absolute difference of the two is 45cm³ what is the probability of a type 1 error?

    She’s been working at this for 5 hours apparently, and neither her or her friends have any idea.

    duntstick
    Free Member

    And it needs to be for a ‘t’ test not ‘z’ test……………

    What language even is this?

    scaredypants
    Full Member

    standard errors ‘n’shit, innit ?

    (that’s as far as my massive knowledge goes though)

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    donncha
    Full Member

    5%
    If we want to be 95% confidentr of rejecting the null hypothesis then there is a 5% chance we might make an error
    Means & SDs are irrelevant

    scaredypants
    Full Member

    Oh, maybe they’re supposed to shove the figures in using various “T” factors and see which one just gets it right ?

    If the absolute difference is changed to 45, then at least one of the samples must have changed and so you couldn’t rely on the SDs or means

    (I iz not a sassystishan)

    scaredypants
    Full Member

    donncha – they’d only know that it was (less than) 5% if they used the values of T corresponding to that confidence limit*. I’m sure it’s possible to calculate the actual CL, but not by me

    *(he speculated)

    duntstick
    Free Member

    What about 45cm cubed bit, was the reply I just got, she managed the CL

    donncha
    Full Member

    from an on-line calculator:
    mean1 eq: 1514.6 (variance= 6146.56) (se= 17.5308)
    mean2 eq: 1553.4 (variance= 5580.09) (se= 16.7034)
    Probability that var1<var2
    p=0.41764 (left: 0.5824; double: 0.8352)
    Difference between means:
    M1-M2=1514.6-1553.4=-38.8
    sd=149.27; se=24.214
    95% CI of difference:
    -86.2593 <-38.8< 8.6593 (Wald)
    t-difference: -1.602
    df-t: 37.5; p= 0.05868
    (left p: 0.9413; two sided: 0.1174)
    Equal sd assumed
    Difference not significant at 5%

    duntstick
    Free Member

    By jove, I think you’ve done it, my Daughter now believes I am a genius and managed all this over a cup of tea and a digestive.

    I will of course own up and give due credit after I have finished basking in the sunshine

    Thanks guys

    donncha
    Full Member

    Dunstick
    What class is this for?

    donncha
    Full Member

    So what was the answer?

    duntstick
    Free Member

    Oh hang on, she reckons that online calculator is for a z test not a t, Donncha, 2nd yr Maths degree statistics

    She got the ci as -17.72 and 95.32

    duntstick
    Free Member

    Does this make any sense?

    duntstick
    Free Member

    Apparently ‘Saying that the means and sds are irrelevant for a type 1 error’ was the crucial bit she was short of

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