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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