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 )
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