In: Statistics and Probability
Solution :
Given that,
Point estimate = s2 = 15.40
n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
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
= 39.364
2R
=
21 -
/2,df = 12.401
The 95% confidence interval for
2 is,
(n - 1)s2 /
2
/2
<
2 < (n - 1)s2 /
21 -
/2
(24) (15.40) / 39.364 <
2 < (24)(15.40) / 12.401
9.39 <
2 < 29.80
(9.39 , 29.80)
s2 = 15.40
n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
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
= 39.364
2R
=
21 -
/2,df = 12.401
The 95% confidence interval for
is,
(n
- 1)s2 /
2
/2
<
<
(n - 1)s2 /
21 -
/2
(24)(15.40)
/ 39.364 <
<
(24)(15.40) / 12.401
3.06 <
< 5.46
(3.06 , 5.46)