Use technology to construct the confidence intervals for the population variance
ID: 2948421 • Letter: U
Question
Use technology to construct the confidence intervals for the population variance
sigma?squared2
and the population standard deviation
sigma?.
Assume the sample is taken from a normally distributed population.
cequals=0.980.98 ,
ssquared2equals=12.2512.25 ,
nequals=2626
The confidence interval for the population variance is
(nothing ,nothing ).
(Round to two decimal places as needed.)
The confidence interval for the population standard deviation is
(nothing ,nothing ).
(Round to two decimal places as needed.)
Explanation / Answer
sigma^2= 0.98
n= 26
s^2= 12.25
alpha= 0.05
chisq(a/2,n-1)
chisq(0.05/2,26-1)
=CHIINV(1-0.05/2,26-1)
13.1197
chisq(1-a/2,n-1)
=chisq(1-0.05/2,26-1)
(CHISQ.INV.RT(0.05/2,26-1))
40.6465
lower limit for popn varince
(n-1)*s^2 / chisq(a/2,n-1)
=(26-1)*12.25/40.6465
7.53
upper limit for popn variance
(n-1)*s^2 / chisq(1-a/2,n-1)
=(26-1)*12.25/13.1197
23.34
CI for popn s.d.
lower= =SQRT(7.534474) = 2.74
upper= =SQRT(23.342759) = 4.83
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