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Testing of population variance

  1. Nov 29, 2017 #1
    1. The problem statement, all variables and given/known data
    with an individual lines at its various windows , a post office finds that the standard deviation for normally distributed waiting times for customers on Friday afternoon is 7.2 minutes . The post office expreiemets with a single, main waiting line and finds that for a random sample of 25 customers, the waiting times for customers have a standard deviation of 3.5 minutes.with a significance level of 5% , test the claim that a single line cause lower variation among waiting times for customers





    2. Relevant equations


    3. The attempt at a solution
    my chi square test value = 5.67 , but teh chi sqaure critical at α = 0.05 and v = 24 is 36.415 , i do n't have enough evidenvce to reject H0 ,
    H0 = 7.2
    H1= <7.2 ,

    But the ans provided is REJECT H0 , why ?

    I think the ans provided is incorrect , correct me if i am wrong .
     
    Last edited by a moderator: Nov 29, 2017
  2. jcsd
  3. Nov 29, 2017 #2

    mjc123

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    What do you mean by H0 = 7.2? If the question is "Can we say that there is significant improvement...?" then surely H0 = 0 (i.e. difference between means = 0 quintals).
    I'm not sure what you've been doing, but I don't think chi-square is the right test for this. Try a t-test.
     
  4. Nov 29, 2017 #3
    question edited , refer back
     
  5. Nov 29, 2017 #4

    mjc123

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    And the question is...?
     
  6. Nov 29, 2017 #5
    with a significance level of 5% , test the claim that a single line cause lower variation among waiting times for customers
     
  7. Nov 29, 2017 #6

    mjc123

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    Please don't edit your original post like that - it makes my posts meaningless to anyone else reading the thread. To make a significant correction like yours you should put it in a new post.
    I still don't understand what you're doing with the chi-squared. This looks like a case for an F-test.
     
  8. Nov 29, 2017 #7

    Ray Vickson

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    You are wrong, but I cannot tell why because you do not give enough details.

    (1) Your H0 and H1 are correct; you are correct in trying to use the ch-squared distribution.
    (2) Exactly how did you compute your so-called "chi-squared" value? I cannot get a number like your 5.67.
    (3) Exactly what test did you perform? Just saying "chi-square" without giving formulas is no help at all.
    (4) I get that H0 is strongly rejected---about as strongly rejected as anything I have ever seen in my life, so strongly rejected as to be virtually impossible.
     
  9. Nov 29, 2017 #8

    WWGD

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    Shouldn't this be an F-test for equality of variances? Where does the ##\chi^2 ## come from?
     
  10. Nov 29, 2017 #9

    Ray Vickson

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    The F-test is for comparing two sample variances. In the current problem, we are given the value of one variance exactly, as if it had infinitely many degrees of freedom (or that is the implication we are probably supposed to make). So the ratio involves ##F(24,\infty) = \chi^2(24).##
     
  11. Nov 29, 2017 #10

    WWGD

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    Ah, yes, ANOVA, my bad.
     
  12. Nov 29, 2017 #11
    Sorry , i have uploded an image so that the concept is more clear .. P/s : I have posted my working inside the photo (beside the formula)
     

    Attached Files:

  13. Nov 29, 2017 #12

    Ray Vickson

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    I don't look at posted images; just type it out.
     
  14. Nov 29, 2017 #13
    chi square test = (n-1)(sample standard deviation^2) / (population standard deviation ^2)
    chi square test = (25-1)(3.5^2) / (7.2^2)= 5.67
     
  15. Nov 29, 2017 #14

    Ray Vickson

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    OK, so then? What do you do next? What number related to the ##\chi^2(24)## do you use now? In post #1 you said you used 36.415. Why?
     
  16. Nov 29, 2017 #15
    As pointed out earlier , chi square value when α = 0.05 and v = 24 is 36.415 , but chi square test value = 5.67 , so we need to reject H0 when chi square test > chi square critical ...
    So , my ans is do not reject Ho

    Anything wrong with my answer ?
     
  17. Nov 29, 2017 #16

    WWGD

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    Look at the statement of your ##H_0, H_A##.
     
  18. Nov 29, 2017 #17
    huh
    nuh ?
     
  19. Nov 29, 2017 #18

    WWGD

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    Domani, mi amico , dovo sortire de la Starbucks adesso. Chi vediamo ( Chi parlamo domani)
     
  20. Nov 29, 2017 #19
    ????
     
  21. Nov 29, 2017 #20

    Ray Vickson

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    Yes, you are badly on the wrong track. However, I must leave it up to you to find your error; if I say any more I will be violating PF rules about giving away answers.
     
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