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.
Solution :
Given that,
s = 0.63
s2 = 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
2L
=
2
/2,df = 128.422
2R
=
21 -
/2,df = 73.361
The 95% confidence interval for
is,
(n
- 1)s2 /
2
/2 <
<
(n - 1)s2 /
21 -
/2
99 * 0.3969 / 128.422 <
<
99 * 0.3969 / 73.361
0.55 <
< 0.73
( 0.55 ,0.73 )
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