In: Statistics and Probability
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. Nicotine in menthol cigarettes 90% confidence; nequals23, sequals0.24 mg.
Solution :
Given that,
n = 23
df = 23 - 1 = 22
s = 0.24
s2 = 0.0576
2L
=
2
/2,df
= 33.924
2R
=
21 -
/2,df = 12.338
The 90% confidence interval for
is,
(n
- 1)s2 /
2
/2
<
<
(n - 1)s2 /
21 -
/2
22
* 0.0576 / 33.924 <
<
22 * 0.0576 / 12.338
0.19 <
< 0.32
(0.19 , 0.32)