The log return X on a certain stock investment is an N(μ,σ2) random variable.A financial analyst has claimed that the volatility σ of the log return on this stock is less than 3 units. A random sample of 11 returns on this stock gave an estimated variance of the log-returns as s2=16.Assess the analyst's claim by using a significance test at level α=0.05 to testH0:σ2≤9 against H1:σ2&gt;9.Find a two-sided 95% confidence interval for σ2.

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The log return X on a certain stock investment is an N(μ,σ2) random variable.A financial analyst has claimed that the volatility σ of the log return on this stock is less than 3 units. A random sample of 11 returns on this stock gave an estimated variance of the log-returns as s2=16.Assess the analyst&#039;s claim by using a significance test at level α=0.05 to testH0:σ2≤9 against H1:σ2&amp;gt;9.Find a two-sided 95% confidence interval for σ2.

benedictazk · Accepted Answer

Since            (      n      −      1      )              S        2                    σ      2        =            10              S        2                    σ      2        ∼      χ          11      −      1        2    =      χ          10        2    ,you have  Pr      (    A    &amp;lt;                  (        n        −        1        )                  S          2                            σ        2              &amp;lt;    B    )    =  0.95where A and B are so chosen that  Pr  (      χ          10        2    &amp;lt;  A  )  =  0.025  =  Pr  (      χ          10        2    &amp;gt;  B  )  .(You can get A and B from tables or software.)Via simple algebra it follows that  Pr      (          1      B        &amp;lt;                  σ        2                    10                  S          2                      &amp;lt;          1      A        )    =  0.95  ,whence  Pr      (                  10                  S          2                    B        &amp;lt;          σ      2        &amp;lt;                  10                  S          2                    A        )    =  0.95.So there&#039;s your confidence interval.If 9 is less than the lower end of this confidence interval, you&#039;d reject the null hypothesis at the 2.5% level. So instead of half of 5% that we used above, use half of 10%, and that will tell you whether to reject the null hypothesis at the 5% level.

The log return X on a certain stock investment is an N(μ,σ2) random variable. A financial analyst h

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