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Math Help - Basic Hypothesis Testing

  1. #1
    Super Member Quacky's Avatar
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    Basic Hypothesis Testing

    A sample of 10 seeds are tested to see if the proportion of seeds that germinates one winter has reduced from the usual value of 0.85. Find the critical region for a one-tailed test using a 5% significance level.

    Answer: x\leq6

    Last edited by Quacky; March 25th 2010 at 05:00 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    since n=10 is small you must use the binomial distribution and not approximate this via a normal

    =.85" alt="H_0=.85" /> vs <.85" alt="H_a<.85" />

    I doubt we will get exactly .05

    \alpha=P(X\le c) where X is a binomial rv with n=10 and p=.85


    DARN close............. P(X\le 6)\approx .049969798878515
    at http://stattrek.com/Tables/Binomial.aspx

    and u still have an inferior duck
    Last edited by matheagle; March 26th 2010 at 06:26 AM.
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  3. #3
    Super Member Quacky's Avatar
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    Thanks for the reply, I had posted this before seeing it.

    Another which I don't understand:

    'My research shows that 3 out of 10 children say their favourite colour is red' announced the professor but Miss Smith believed that the proportion was much higher. She asked 6 students, 3 of whom had red as their favourite. She uses a 5% significance level.

    a) Test Miss Smith's belief on the basis of this sample (a: He belief at the 5% significance level is unfounded.)
    b) She decides to use a larger sample of 20 students. Find how many must choose red as their favourite colour for Miss Smith to have a significant result. (answer: 12)

    Edit: I'll get round to updating the avatar soon...
    Last edited by Quacky; March 26th 2010 at 08:17 AM.
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  4. #4
    MHF Contributor matheagle's Avatar
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    =.3" alt="H_0=.3" /> vs >.3" alt="H_a>.3" />

    Here Our rv X is binomial with n=6 and we assume p=.3 to obtain alpha.

    \alpha=P(X\ge c)

    If she observes 3 I would calculate the p-value as

    P(X\ge 3)\approx .25569 which is not significant at alpha equal to .05.


    As for n=20 I still would use the binomial and not approximate this with a normal.
    and I don't see x=12 as the answer here...

    If X is Bin(n=20, p=.3), then P(X\ge 12)\approx 0.00513816153512103
    Last edited by matheagle; March 27th 2010 at 08:01 AM.
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