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)