Question

A simple random sample from a population with a normal distribution of 100 body temperatures has x=98.90 degrees Upper F°F and s=0.63 degrees Upper F°F. Construct an 95% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

Answer #1

Solution :

Given that,

s = 0.63

s^{2} = 0.3969

n = 100

Degrees of freedom = df = n - 1 = 100 - 1 = 99

At 95% confidence level the
^{2} value is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

1 - / 2 = 1 - 0.025 = 0.975

^{2}_{L}
=
^{2}_{/2,df} = 128.422

^{2}_{R}
=
^{2}_{1 -} _{/2,df} = 73.361

The 95% confidence interval for is,

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

99 * 0.3969 / 128.422 < < 99 * 0.3969 / 73.361

0.55 < < 0.73

( 0.55 ,0.73 )

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