Question

Use technology to construct the confidence intervals for the population variance sigmasquared and the population standard deviation sigma. Assume the sample is taken from a normally distributed population. c=0.95, s=34, n=16

Answer #1

Solution :

Given that,

s = 34

Point estimate = s^{2} = 1156

^{2}_{R}
=
^{2}_{/2,df}
= 27.488

^{2}_{L}
=
^{2}_{1 -} _{
/2,df} = 6.262

The 95% confidence interval for
^{2} is,

(n - 1)s^{2} /
^{2}_{/2}
<
^{2} < (n - 1)s^{2} /
^{2}_{1 -} _{
/2}

(15)(1156) / 27.488 <
^{2} < (15)(1156) / 6.262

630.81 <
^{2} < 2769.04

**(630.81 , 2769.04)**

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