Use the given information to find the number of degrees of f

Use the given information to find the number of degrees of freedom, the critical values Superscript 22L and Superscript 22R, and the confidence interval estimate of .It is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.

Nicotine in menthol cigarettes 80% confidence; n=30, sequals=0.28mg.

df=(__)(Type a whole number.)

Superscript 22L=(__) (Round to three decimal places as needed.)

Superscript 22R=(__) (Round to three decimal places as needed.)

The confidence interval estimate of is (__) mg <<mg.

(Round to two decimal places as needed.)

Solution

Confidence Interval
CI = (n-1) S^2 / ^2 right < ^2 < (n-1) S^2 / ^2 left
Where,
S = Standard Deviation
^2 right = (1 - Confidence Level)/2
^2 left = 1 - ^2 right
n = Sample Size

Since aplha =0.02
^2 right = (1 - Confidence Level)/2 = (1 - 0.98)/2 = 0.02/2 = 0.01
^2 left = 1 - ^2 right = 1 - 0.01 = 0.99
the two critical values ^2 left, ^2 right at 29 df are 49.5879 , 14.256
S.D( S^2 )=0.28
Sample Size(n)=30
Confidence Interval = [ 29 * 0.0784/49.5879 < ^2 < 29 * 0.0784/14.256 ]
= [ 2.2736/49.5879 < ^2 < 2.2736/14.2565 ]
Confidence Interval S.D = [ Sqrt(0.0458) < < Sqrt(0.1595) ] = [ 0.214,0.3993]