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Math Help - understanding the meaning of the answer

  1. #1
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    understanding the meaning of the answer

    All the answers to these excercices on hypothesis testing go like this : " therefore reject H_0 at a alfa greater than **(number)** " WHat does it mean? For example, at this last excercice I got that the P-value was 0.0367 and alfa was 0.05 and H_1 was >. So P should have been > than alfa. But this was not the case, and I rejected. I go and see the answer and the book says "therefore reject H_0 at a alfa greater than 3.67%" What does it mean at a alfa greater then ..? And shall I always say that in my solution?


    Thank you so much.
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  2. #2
    Member Glaysher's Avatar
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    Quote Originally Posted by 0123 View Post
    All the answers to these excercices on hypothesis testing go like this : " therefore reject H_0 at a alfa greater than **(number)** " WHat does it mean? For example, at this last excercice I got that the P-value was 0.0367 and alfa was 0.05 and H_1 was >. So P should have been > than alfa. But this was not the case, and I rejected. I go and see the answer and the book says "therefore reject H_0 at a alfa greater than 3.67%" What does it mean at a alfa greater then ..? And shall I always say that in my solution?


    Thank you so much.
    Your probability is less than the significance level and therefore your result is significant. This means that you reject the null hypothesis in favour of the alternative hypothesis
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    Quote Originally Posted by Glaysher View Post
    Your probability is less than the significance level and therefore your result is significant. This means that you reject the null hypothesis in favour of the alternative hypothesis
    So you mean, I have a probability 3.67% that H_0 is true, but we said "No! We want the treshold to be 5%! Less than 5% we do not accept anything!" But you say "but the true probability to get H_0 true is 3.67 % from the p-value" "3.67%? Too low!Reject H_0!"

    Is this it? I know the way I say it is really inappropriate (and embarassing), but I do it when I really have hard hard time understanding..

    Thanks for your help.
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  4. #4
    Member Glaysher's Avatar
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    Quote Originally Posted by 0123 View Post
    So you mean, I have a probability 3.67% that H_0 is true, but we said "No! We want the treshold to be 5%! Less than 5% we do not accept anything!" But you say "but the true probability to get H_0 true is 3.67 % from the p-value" "3.67%? Too low!Reject H_0!"

    Is this it? I know the way I say it is really inappropriate (and embarassing), but I do it when I really have hard hard time understanding..

    Thanks for your help.
    No, more like 3.67% chance of getting the observed value given that H_0 is true. Because this is less than 5% we judge it to be too unlikely to have happened and reject H_0 in favour of H_1
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    Quote Originally Posted by Glaysher View Post
    No, more like 3.67% chance of getting the observed value given that H_0 is true. Because this is less than 5% we judge it to be too unlikely to have happened and reject H_0 in favour of H_1
    Sorry, I am afraid I do not understand. You mean, our computation revealed that , given H_0 true, we get that value about 3.67% of the times. But If H_0 was true we expected the value to happen at least 5% of times. SO we infer that H_0 cannot be true. Is this it? Thank you.
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  6. #6
    Member Glaysher's Avatar
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    Quote Originally Posted by 0123 View Post
    Sorry, I am afraid I do not understand. You mean, our computation revealed that , given H_0 true, we get that value about 3.67% of the times. But If H_0 was true we expected the value to happen at least 5% of times. SO we infer that H_0 cannot be true. Is this it? Thank you.
    If you give me an example to go through it will be easier to explain as hypothesis testing can be used in a variety of circumstances

    One example could be:

    Pepsi claim their coke is better than Coca Cola. Fifteen out of twenty people who participated in a taste test claimed Pepsi was better. Perform a hypothesis test at the 5% level to test this claim

    Assuming that the people's choices were 50/50 this can be modelled by:

    X~B(20,0.5)

    Giving hypotheses:

    H_0 = 0.5
    ie there is no difference between Pepsi and Coca Cola

    H_1 > 0.5
    ie Pepsi is better

    We assume H_0 to be true

    We calculate the probability of getting the observed value or more as we check the ends of the distribution (the probability of getting the exact observed value being small anyway)

    P(X > 15) = 1 - P(X < 14) = 1 - 0.9793 = 0.0207

    We compare this probability with our 5%

    0.0207 < 0.05

    Since the probability is less than 5% we judge it to be unlikely to have happened given our initial assumption. Therefore the initial assumption is wrong. Therefore reject H_0 in favour of H_1. The evidence suggests Pepsi's claim is true
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