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Thread: Statistics Marathon & Questions

  1. #51
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    Re: University Statistics Discussion Marathon

    Me too I've been thinking about it for a few days......................im guessing it would be lower. I read somewhere if you increase the sample size the p-value decreases slightly.
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by davidgoes4wce View Post
    Me too I've been thinking about it for a few days......................im guessing it would be lower. I read somewhere if you increase the sample size the p-value decreases slightly.
    If the mean or SD didn't change, that means the Z score probably didn't change right ?

    If that doesn't change, the p value doesn't change too .
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by nerdasdasd View Post
    If the mean or SD didn't change, that means the Z score probably didn't change right ?

    If that doesn't change, the p value doesn't change too .
    OK I'll take your word for it. I'll look to read up on it a bit further as I have actually never thought it about it in too much detail.
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    Re: University Statistics Discussion Marathon

    My stats knowledge is minimal, but wouldn't it decrease?

    I assume that whats going on is you have the hypothesis that the avg sleeping hours of a student are normally distributed with mean 8 and variance V. We are doing a one-tailed test with test statistic our sample mean.

    If our p-value is 0.1 that means the observed sample mean m of our initial sample of 20 students is quite a bit less than 8. (So the probability of a randomly selected student from our population sleeping less than m hours on average is only 0.1).

    But the distribution of sample means in samples of size n is given by N(8,V/n). So as n increases, the probability of the the test statistic being smaller than m decreases, i.e. the p-value decreases.


    Is there some other choice of hypothesis/test statistic here? Without specifying such a choice, the one I have made above seems natural to me.
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by seanieg89 View Post
    My stats knowledge is minimal, but wouldn't it decrease?

    I assume that whats going on is you have the hypothesis that the avg sleeping hours of a student are normally distributed with mean 8 and variance V. We are doing a one-tailed test with test statistic our sample mean.

    If our p-value is 0.1 that means the observed sample mean m of our initial sample of 20 students is quite a bit less than 8. (So the probability of a randomly selected student from our population sleeping less than m hours on average is only 0.1).

    But the distribution of sample means in samples of size n is given by N(8,V/n). So as n increases, the probability of the the test statistic being smaller than m decreases, i.e. the p-value decreases.


    Is there some other choice of hypothesis/test statistic here? Without specifying such a choice, the one I have made above seems natural to me.
    With these MCQ questions (they were given to UNSW business statistics students)

    The section or topic of the quiz , the majority of the questions were based on the t-test.

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    Re: University Statistics Discussion Marathon

    The more I think about it the more I think the P-Value actually decreases



    Case 1:







    Case 2:








    So what I can interpret from this is it decreases.
    Last edited by davidgoes4wce; 1 Jun 2016 at 5:23 PM.
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    Re: University Statistics Discussion Marathon

    Also I will admit , I did not know how to calculate a P-Value manually up until last week. (having studied high school stats+ uni stats for around 6 years) If you guys are looking to get better at statistics with Excel highly recommend this book by : Mark Berenson, David Levine and Kathryn Szabat, BUSS1020 Quantitative Business Analysis.

    I personally feel they explain stats better than the Science, Advanced Science, Engineering or Psychology way of statistics.
    Last edited by davidgoes4wce; 1 Jun 2016 at 5:22 PM.
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    Re: University Statistics Discussion Marathon

    Sure, if you are using the t-test then use that formula instead, it will still decrease. You can compute the p-value in terms of n by using the t-distribution and show it decreases by using calculus or whatever else you like.

    Just think about it intuitively, a sample of two students who on average undersleep by H hours is far less significant than a sample of 1,000,000 students who on average undersleep by the same amount. (With both samples having the same s.d.)

    The latter is far greater evidence of a trend of undersleeping students, and any reasonable statistical test should reflect this.
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    Re: University Statistics Discussion Marathon






    Ans : 11.7
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    Re: University Statistics Discussion Marathon

    This is the theory behind the above question



    It seems like in that 2nd line of working, they did an expansion, I for one could not see that expansion of








    I got a bit lost with the 'n' chucked in the third term of the expansion as well.
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    University Statistics Discussion Marathon

    Expand the square and note that the mean (and also its square) is a constant.

    In the second summand there is a common factor which can be factorised out.

    In the third summand note that you are summing the same constant value n times.
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by davidgoes4wce View Post





    Ans : 11.7
















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    Re: University Statistics Discussion Marathon

    Here is something more theoretical.

    Suppose for j=1,...,n are i.i.d random variables for some unknown parameters .

    1. Define

    Compute

    2. Hence define in terms of a random variable that has expected value and variance . Compute the pdf of this random variable in terms of special functions.

    3. What happens as ? Prove this.


    (This question outlines some of the theory behind something used several times in this thread.)
    Last edited by seanieg89; 2 Jun 2016 at 2:52 PM.

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    Re: University Statistics Discussion Marathon

    Can you guys stop dropping the big guns... you're making statistics look hard.

  15. #65
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by BlueGas View Post
    Can you guys stop dropping the big guns... you're making statistics look hard.
    Huh? Not all of statistics is just plugging numbers into memorised formulae, where do you think these formulae come from?

    As always, you have the option of ignoring any question not to your taste.

    In any case, this particular question is easier than most of the mathematical questions posted in these forums.

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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by seanieg89 View Post
    Here is something more theoretical.

    Suppose for j=1,...,n are i.i.d random variables for some unknown parameters .

    1. Define

    Compute

    2. Hence define in terms of a random variable that has expected value and variance . Compute the pdf of this random variable in terms of special functions.

    3. What happens as ? Prove this.


    (This question outlines some of the theory behind something used several times in this thread.)






















































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    Supreme Member seanieg89's Avatar
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    Re: University Statistics Discussion Marathon

    Yep good stuff, it remains to compute Var(s^2), but what you have done is enough to motivate the later parts of the question so don't worry about that if you don't want to.

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    Re: University Statistics Discussion Marathon

    Screen Shot 2016-06-04 at 11.14.13 pm.zip

    Can someone explain for me please

  19. #69
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by edwardjoh2 View Post
    Screen Shot 2016-06-04 at 11.14.13 pm.zip

    Can someone explain for me please
    That's dodgy. Please leave the screenshot in the form of an actual image. I don't want to risk getting an infection.
    If I am a conic section, then my e = ∞

    Just so we don't have this discussion in the future, my definition of the natural numbers includes 0.

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    Re: University Statistics Discussion Marathon













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    Re: University Statistics Discussion Marathon

    Im thinking the answer is E ( I don't have the solution on me ) Here is my explanation and thinking.









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    Re: University Statistics Discussion Marathon











    Last edited by davidgoes4wce; 5 Jun 2016 at 3:56 PM.
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    Re: University Statistics Discussion Marathon

    A sample of 50 observation is taken from a normal population, with mean of 100 and Standard Deviation 10. If the population is finite with N=250

    Find

    P(xbar > 103)

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  24. #74
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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by Rhinoz8142 View Post
    A sample of 50 observation is taken from a normal population, with mean of 100 and Standard Deviation 10. If the population is finite with N=250

    Find

    P(xbar > 103)








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    Re: University Statistics Discussion Marathon

    Quote Originally Posted by Rhinoz8142 View Post
    A sample of 50 observation is taken from a normal population, with mean of 100 and Standard Deviation 10. If the population is finite with N=250

    Find

    P(xbar > 103)


    then compute the value from there. Note that the population size is not relevant here as we are referring to the distribution of the sample mean.

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