Question

Use the given information to find the number of degrees of​ freedom, the critical values chi Subscript Upper L Superscript 2χ2L and chi Subscript Upper R Superscript 2χ2R​, and the confidence interval estimate of sigmaσ. 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=27​, s=65.9.

Answer 1

Solution :

Given that,

c = 0.99

s = 65.9

n = 27

At 99% confidence level the is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_/2,df = _0.005,26 = 48.29

and

_{1- /2,df} = _0.995,26 = 11.16

²_L = ²_/2,df = 48.29

²_R = ²_{1 - /2,df} = 11.16

The 99% confidence interval for is,

s (n-1) / _/2,df < < s (n-1) / _{1- /2,df}

65.9( 27 - 1 ) / 48.29< < 65.9( 27- 1 ) / 11.16

48.36 < < 100.59

( 48.36 , 100.59)