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Math Help - Choosing the correct null hypothesis.

  1. #1
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    Choosing the correct null hypothesis.

    I have a load of sample data on bike hires on the Barclays Bicycle Hire Scheme.

    I need to do a hypothesis test to see whether the true population mean is in line with London Transports expectation that bikes should be hired for no longer than 60 minutes.

    I put down that:

    H0: Mean >= 60
    H1: Mean < 60

    Is this correct? People keep telling me it's the other way round but I was under the impression that the null is the hypothesis you're looking to reject?

    Yes I have seen the sticky just wanted some clarification.
    Last edited by Wevans2303; March 21st 2012 at 09:51 AM.
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  2. #2
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    Re: Choosing the correct null hypothesis.

    Hi Wevans, The null hypothesis is that the initial supposition is true, in this case that bike hire is on average < 60 minutes. If your data supported this supposition then you would have no evidence to reject the null hypothesis. Its not so much a question of which hypothesis you want to reject as it is asking: what is the probability (p-value) that two samples come from the same distribution (the null hypothesis)? Or in your case, the probability that your data (sample) comes from a population (all hires) whose true mean is < 60 mins. If this probability is very low (usually taken to be a probability< 0.05, arbitrarily I might add) then this is taken as evidence that the samples come do not come from the same distribution. Notice that at this p-value threshold (0.05) one in twenty times when samples do come from the same distribution you will incorrectly reject the null hypothesis. Hence why the smaller your p-value is the stronger is the evidence for rejecting the null.

    Be careful to distinguish between a sample and a population. If you have all the data for all bike-hires, then there is no "test" to do; simply calculate the population mean. It is what it is. If however you only have a sample, the question is whether this is representative of the true population. This is the root of much controversy in medical statistics, since it is very easy to select an unrepresentative sample from the population and very hard to select a representative one.

    I hope that is a bit clearer. MD
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  3. #3
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    Re: Choosing the correct null hypothesis.

    People keep telling me it's the other way round
    I think either way round is acceptable in this case.
    Last edited by SpringFan25; March 22nd 2012 at 01:52 PM.
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  4. #4
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    Re: Choosing the correct null hypothesis.

    Quote Originally Posted by Mathsdog View Post
    Hi Wevans, The null hypothesis is that the initial supposition is true, in this case that bike hire is on average < 60 minutes. If your data supported this supposition then you would have no evidence to reject the null hypothesis. Its not so much a question of which hypothesis you want to reject as it is asking: what is the probability (p-value) that two samples come from the same distribution (the null hypothesis)? Or in your case, the probability that your data (sample) comes from a population (all hires) whose true mean is < 60 mins. If this probability is very low (usually taken to be a probability< 0.05, arbitrarily I might add) then this is taken as evidence that the samples come do not come from the same distribution. Notice that at this p-value threshold (0.05) one in twenty times when samples do come from the same distribution you will incorrectly reject the null hypothesis. Hence why the smaller your p-value is the stronger is the evidence for rejecting the null.

    Be careful to distinguish between a sample and a population. If you have all the data for all bike-hires, then there is no "test" to do; simply calculate the population mean. It is what it is. If however you only have a sample, the question is whether this is representative of the true population. This is the root of much controversy in medical statistics, since it is very easy to select an unrepresentative sample from the population and very hard to select a representative one.

    I hope that is a bit clearer. MD
    Hmm, I thought the null was always the thing you set out to disprove in favour of the alternative hypothesis, after all you need to find supportive evidence that the claim is in fact true?

    Quote Originally Posted by SpringFan25 View Post
    I think either way round is acceptable in this case.
    I was under the impression it was always extremely important to make sure you get it the right way round.
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  5. #5
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    Re: Choosing the correct null hypothesis.

    I was under the impression it was always extremely important to make sure you get it the right way round.

    normally i would agree with you. But this is an unusual since your null is a range (not a point) and you are doign a 1 tailed test.

    we have to choose between:
    [Test A]H0:mean >= 60, H1: mean<60
    [Test B]H0:mean <= 60, H1: mean>60

    is there any value of the sameple mean that would make you reach a different conclusion with test [A] than test [B]? i cant think of one, so i think it makes no difference in this case.
    Last edited by SpringFan25; March 23rd 2012 at 11:59 AM.
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