Question

Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place.

n=23n=23, s=4.4s=4.4, and c=0.98

Answer 1

Sol:

df=n-1=23-1=22

alpha=1-0.98=0.02

alpha/2=0.02/2=0.01

a-alpha/2=1-0.01=0.99

chi sq alpha/2==CHISQ.INV.RT(0.01,22)=40.28936044

chi sq 1-alpha/2==CHISQ.INV.RT(0.99,22)=9.542492339

98% confidence interval for population standard deviation

sqrt((n-1)*s^2/chi sq(alpha/2)<sigma<sqrt((n-1)*s^2/chi sq(1-alpha/2)

sqrt((23-1)*4.4^2/40.28936044)<sigma<sqrt((23-1)*4.4^2/9.542492339))

3.251388<sigma<6.680871

3.3<sigma<6.7

ANSWER;

98% lower limit sigma=3.3

98% upper limit sigma=6.7

3.3<sigma<6.7