Question

Question 3 [Points 6]. Topic: Two sided Confidence Interval estimate on population standard deviation The weights of 22 randomly selected eggs have a sample mean of 1.78 oz and a standard deviation, s, of 0.42 oz. a) Determine the 95% 2-sided confidence interval for the standard deviation, o, of the weights of all eggs. Choose an answer from the below choices. A. 0.34 to 0.57 oz C. 0.32 to 0.60 oz B. 0.32 to 0.58 oz D. 0.33 to 0.55 oz b) Perform the interpretation of the answer obtained. Write the interpretation in clear English.

Answer 1

Here s = 0.42 and n = 22
df = 22 - 1 = 21

α = 1 - 0.95 = 0.05
The critical values for α = 0.05 and df = 21 are Χ^2(1-α/2,n-1) = 10.283 and Χ^2(α/2,n-1) = 35.479

(n-1)Kostn"15 (n - 1)s xảya - xỉ a/2

CI = (sqrt(21*0.42^2/35.479) , sqrt(21*0.42^2/10.283))
CI = (0.32 , 0.6)

OPtion c)

b)

we are 95% confident that the standard deviation is between 0.32 and 0.60