Question

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.

Platelet Counts of Women 80​% ​confidence; n = 25​, s = 65.9.

df =

χ2_L (chi Subscript Upper L Superscript 2) =

X_R² (chi Subscript Upper R Superscript 2) =

The confidence interval estimate of sigma is ___ mg < sigma < ___ mg.

Answer 1

Given

n = 25

So degrees of freedom = n - 1 = 25 -1

d.f= 24

For c = confidence level = 0.80

² critical values are

  ²_{a/2 , n -1 =} ²0.10,24 = 33.196

²1-a/2 , n -1= ², 0.90,24 = 15.659

The 80% confidence interval for population standard deviation is

sqrt( (n -1)*s^{​​​​​​2}​​​/²,0.10,24 ) < < sqrt((n-1)*s^{​​​​​​2}/²,0.90,24)

sqrt(24* 65.9²/33.196) <   < sqrt(24*65.9²/15.659)

65.03 < < 81.58