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Math Help - Test on a single proportion

  1. #1
    Junior Member
    Joined
    Nov 2009
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    60

    Question Test on a single proportion

    A marketing expert for a pasta-making company believes that 40% of pasta lovers prefer lasagna. If 9 out of 20 pasta lovers choose lasagna over other pastas, what can be concluded about the expertís claim? Use a 0.05 level of significance.

    (Textbook Ans : P-value = 0.4044 (with a one-tailed test); the claim is not refuted).

    Using binomial distribution to get the P-Value, i have n=10,p=0.40, r=9 and so my answer = 2x 0.7553 (looking up the table) = 1.5106.
    (while textbook ans is 0.4044)

    so where have i gone wrong ?
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  2. #2
    Newbie
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    Sep 2012
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    guatemala
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    Re: Test on a single proportion

    My solution emiranda:
    Ho: p = 0.4
    H1: p > 0.4
    Since n = 20, not large enough to use normal approximation for z test statistic.
    X: No. of pasta lovers choose lasagna
    X ~ Bin (20,0.4)
    Since x = 9 > 20(0.4) = 8
    P = (X>=9) = 1-(X<9)=1-0.5956(from table) = 0.4044
    Since P > α=0.05, accept Ho.
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