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Math Help - hypothesis testing help

  1. #1
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    hypothesis testing help

    1. Test the assertion (at alpha 0.05) that it rains more often on weekends than it does on weekdays if in a sample of 31 rainy days, 10 were either saturday or sunday?

    ----
    is my answer right?

    n = 31
    p = 2/7
    q = 5/7

    h0: p = 2/7
    h1: p < 2/7

    the zscore turns out to be 0.45, so we reject h0 and accept 1 (does not rain more often on weekends)?

    2. In a taste test, 15 of 25 people choose beverage X over beverage y. Is this significant evidence to conclude that people prefer X to Y?

    is p = 1/2 in this one and i would just make up an alpha value like 0.02?
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  2. #2
    MHF Contributor
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    (a)
    The test is right.

    X \sim Bi(31,2/7)

    P(X \geq 10) = 0.0088

    You are interested in deviations where x is too high, so this is a 1 tailed test.

    0.0088 is far lower than the significance level (0.05), so reject H0. Be very careful about saying you accept H1. Saying H0 is false is not the same as saying H1 is true, except in special cases where H1 is "H0 is false".


    I'm not familiar with the "z-score" notation so i dont know if that is the same as your answer


    (b)
    yes
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