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a simple random sample of size 20 is drawn from a population that is known to be

ID: 3153996 • Letter: A

Question

a simple random sample of size 20 is drawn from a population that is known to be normally distributed. The sample variance, s2 , is determined to be 13.2 . construct a 90% confidence interval for a2. the lower bound is? a simple random sample of size 20 is drawn from a population that is known to be normally distributed. The sample variance, s2 , is determined to be 13.2 . construct a 90% confidence interval for a2. the lower bound is? a simple random sample of size 20 is drawn from a population that is known to be normally distributed. The sample variance, s2 , is determined to be 13.2 . construct a 90% confidence interval for a2. the lower bound is?

Explanation / Answer

As              
              
df = n - 1 =    19          
alpha = (1 - confidence level)/2 =    0.05          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    30.14352721          
chi^2(alpha/2) =    10.11701306          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    8.320194193   [ANSWER, LOWER BOUND]


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Other info:
      
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    24.78992549          
              
Thus, the confidence interval for the variance is              
              
(   8.320194193   ,   24.78992549   )