variance validation











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The scores on a placement test given to college
freshmen for the past five years are approximately normally
distributed with a mean $μ = 74$ and a variance
$σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
value of the variance if a random sample of $20$ students
who take the placement test this year obtain a value of
$s^2 = 20$?



I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?










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    The scores on a placement test given to college
    freshmen for the past five years are approximately normally
    distributed with a mean $μ = 74$ and a variance
    $σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
    value of the variance if a random sample of $20$ students
    who take the placement test this year obtain a value of
    $s^2 = 20$?



    I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?










    share|cite|improve this question
























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      The scores on a placement test given to college
      freshmen for the past five years are approximately normally
      distributed with a mean $μ = 74$ and a variance
      $σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
      value of the variance if a random sample of $20$ students
      who take the placement test this year obtain a value of
      $s^2 = 20$?



      I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?










      share|cite|improve this question













      The scores on a placement test given to college
      freshmen for the past five years are approximately normally
      distributed with a mean $μ = 74$ and a variance
      $σ^2 = 8$. Would you still consider $σ^2 = 8$ to be a valid
      value of the variance if a random sample of $20$ students
      who take the placement test this year obtain a value of
      $s^2 = 20$?



      I think I'm supposed to use the F-distribution somehow in this problem, however, I've only been able to find out how to compare to sample variances--not how to compare a sample variance with a population variance. Any tips on how to solve this?







      statistics






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      asked Feb 9 '15 at 3:21









      hildk

      11




      11






















          1 Answer
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          Hypotheses:



          $H_0: sigma^2 = 8$



          $H_1: sigma^2 neq 8$



          This is a $chi^2$ test for one variance problem.



          Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):




          1. The population has a normal distribution.

          2. The sample is a random sample.


          The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
          I'm not sure what significance level you're using, but from here, it should be pretty straightforward.






          share|cite|improve this answer





















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            1 Answer
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            1 Answer
            1






            active

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            active

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            up vote
            0
            down vote













            Hypotheses:



            $H_0: sigma^2 = 8$



            $H_1: sigma^2 neq 8$



            This is a $chi^2$ test for one variance problem.



            Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):




            1. The population has a normal distribution.

            2. The sample is a random sample.


            The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
            I'm not sure what significance level you're using, but from here, it should be pretty straightforward.






            share|cite|improve this answer

























              up vote
              0
              down vote













              Hypotheses:



              $H_0: sigma^2 = 8$



              $H_1: sigma^2 neq 8$



              This is a $chi^2$ test for one variance problem.



              Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):




              1. The population has a normal distribution.

              2. The sample is a random sample.


              The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
              I'm not sure what significance level you're using, but from here, it should be pretty straightforward.






              share|cite|improve this answer























                up vote
                0
                down vote










                up vote
                0
                down vote









                Hypotheses:



                $H_0: sigma^2 = 8$



                $H_1: sigma^2 neq 8$



                This is a $chi^2$ test for one variance problem.



                Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):




                1. The population has a normal distribution.

                2. The sample is a random sample.


                The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
                I'm not sure what significance level you're using, but from here, it should be pretty straightforward.






                share|cite|improve this answer












                Hypotheses:



                $H_0: sigma^2 = 8$



                $H_1: sigma^2 neq 8$



                This is a $chi^2$ test for one variance problem.



                Assumptions (taken from Statistics Manual by Crow, Davis, Maxfield):




                1. The population has a normal distribution.

                2. The sample is a random sample.


                The test statistic under the null distribution is $$chi^2 = dfrac{(n-1)s^2}{sigma^2} = dfrac{(20-1)(20)}{8} = 47.5text{.}$$
                I'm not sure what significance level you're using, but from here, it should be pretty straightforward.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Feb 9 '15 at 3:43









                Clarinetist

                10.8k42777




                10.8k42777






























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