Question

Use the given information to find the number of degrees of freedom, the critical values chi Subscript Upper L Superscript 2 and chi Subscript Upper R Superscript 2 , and the confidence interval estimate of sigma . It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Platelet Counts of Women 80% confidence; n = 25, s = 65.9.

df =

χ2_{L} (chi Subscript Upper L Superscript 2) =

X_{R}^{2} (chi Subscript Upper R Superscript 2)
=

The confidence interval estimate of sigma is ___ mg < sigma < ___ mg.

Answer #1

Given

n = 25

So degrees of freedom = n - 1 = 25 -1

d.f= 24

For c = confidence level = 0.80

^{2}
critical values are

^{2}_{a/2
, n -1 =}
^{2}0.10,24 = 33.196

^{2}1-a/2
, n -1=
^{2}, 0.90,24 = 15.659

The 80% confidence interval for population standard deviation is

sqrt( (n -1)*s^{2}/^{2},0.10,24
) <
< sqrt((n-1)*s^{2}/^{2},0.90,24)

sqrt(24* 65.9^{2}/33.196) <
< sqrt(24*65.9^{2}/15.659)

65.03 < < 81.58

Use the given information to find the number of degrees of
freedom, the critical values chi Subscript Upper L Superscript 2
and chi Subscript Upper R Superscript 2, and the confidence
interval estimate of sigma. It is reasonable to assume that a
simple random sample has been selected from a population with a
normal distribution. Platelet Counts of Women 95% confidence;
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interval estimate of sigma. It is reasonable to assume that a
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