In: Statistics and Probability
Use the given information to find the number of degrees of freedom, the critical values X^2L and X^2R, and the confidence interval estimate of σ. It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution. Platelet Counts of Women 99% confidence; n=28, s=65.2. What is the degrees of freedom? What is the X^2R and X^2L? What is the standard deviation?
Solution :
Given that,
n = 28
df = 27
2R
=
2
/2,df
= 49.645
2L
=
21 -
/2,df = 11.808
The 99% confidence interval for
is,
(n
- 1)s2 /
2
/2
<
<
(n - 1)s2 /
21 -
/2
27
* 65.22 / 49.645 <
<
27 * 65.22 / 11.808
48.5993 <
< 99.6522
(48.5993 , 99.6522)