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Math Help - Test the hypothesis

  1. #1
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    Test the hypothesis

    Question : A computer system has 6 I/O channels and the system personnel are reasonably certain that the load on channels is balanced. If X is random variable denoting the index of the channel to which a given I/O operations is directed , that its pmf is assumed to be uniformly distributed. Out of N=150 I/O operation onserved, the number of operations directed to various channels were:

    n_0 = 22 ; \  n_1 = 23 ; \ n_2 = 29 ; \ n_3 = 31 ; \ n_4 = 26 ; \ n_5 = 19

    Test the hypothesis that the load on channels is balanced at 5 percent level of significance.
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  2. #2
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    Quote Originally Posted by zorro View Post
    Question : A computer system has 6 I/O channels and the system personnel are reasonably certain that the load on channels is balanced. If X is random variable denoting the index of the channel to which a given I/O operations is directed , that its pmf is assumed to be uniformly distributed. Out of N=150 I/O operation onserved, the number of operations directed to various channels were:

    n_0 = 22 ; \ n_1 = 23 ; \ n_2 = 29 ; \ n_3 = 31 ; \ n_4 = 26 ; \ n_5 = 19

    Test the hypothesis that the load on channels is balanced at 5 percent level of significance.
    You are given a uniform pmf, which mean that p_0 = p_1 = p_2=p_3=p_4=p_5 =\frac{1}{6}

    The expected means \mu_0=\mu_1=\mu_2=\mu_3=\mu_4=\mu_5= Np

    \sigma = \sqrt{Npq}

    Use a two-tailed test at the 0.05 significance level and adapt the following decision rule:

    Accept H_0 if all z scores of the sample mean is inside the range z_{0.05} to z_{0.95} , i.e, all channels are balanced.
    Reject H_0 otherwise.
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  3. #3
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    which test are u using ?

    Quote Originally Posted by novice View Post
    You are given a uniform pmf, which mean that p_0 = p_1 = p_2=p_3=p_4=p_5 =\frac{1}{6}

    The expected means \mu_0=\mu_1=\mu_2=\mu_3=\mu_4=\mu_5= Np

    \sigma = \sqrt{Npq}

    Use a two-tailed test at the 0.05 significance level and adapt the following decision rule:

    Accept H_0 if all z scores of the sample mean is inside the range z_{0.05} to z_{0.95} , i.e, all channels are balanced.
    Reject H_0 otherwise.

    Which test are u using

    And what is 'q' is it '1-p' or some thing else please advice
    Last edited by zorro; December 16th 2009 at 09:26 PM.
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    Quote Originally Posted by zorro View Post
    Which test are u using

    And what is 'q' is it '1-p' or some thing else please advice
    q = 1-p
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  5. #5
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    which test are u using

    Quote Originally Posted by novice View Post
    q = 1-p

    Could u please tell me which test are u using.......is there a link u could provide me ...........just if i encounter similar problems in the future
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    Quote Originally Posted by zorro View Post
    Could u please tell me which test are u using.......is there a link u could provide me ...........just if i encounter similar problems in the future
    You have small sample, Student t-test would be good. If you prefer, you may do F-test, or Chi-square test too.

    Take a look at an example here:

    http://www.mathhelpforum.com/math-he...s-testing.html
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  7. #7
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    I still have questions

    Quote Originally Posted by novice View Post
    You have small sample, Student t-test would be good. If you prefer, you may do F-test, or Chi-square test too.

    Take a look at an example here:

    http://www.mathhelpforum.com/math-he...s-testing.html

    But the student t test is \frac{ \bar X - \mu}{ \sigma / \sqrt{n}} so how are u using \sigma = \sqrt{Npq}
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  8. #8
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    I got it now

    Quote Originally Posted by zorro View Post
    But the student t test is \frac{ \bar X - \mu}{ \sigma / \sqrt{n}} so how are u using \sigma = \sqrt{Npq}

    I got it when X is a binomial distribution and N is very large and probability of individual trails is close to 1/2 is can be seen that with increasing n these distribution approaches a normal distribution which can be expressed as

    z = \frac{X - np}{\sqrt{npq}} as n \to \infty

    Thanks mite
    cheers to every one for helping me with this problem
    Last edited by zorro; December 19th 2009 at 03:14 AM. Reason: Wanted to thank every one who had help me
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