Question

The following data were randomly drawn from an approximately normal population . 25, 25, 28, 32, 34, 38, 41. Based on these data , find a 90% confidence inverval for the population standard deveviation .

Answer 1

	here n =	7
	s2=	39.143
Critical value of chi square distribution for n-1=6 df and 90 % CI
Lower critical value χ2L=		1.635
Upper critical valueχ2U=		12.592

for Confidence interval of standard deviation:
Lower bound =√((n-1)s2/χ2U)=		4.319
Upper bound =√((n-1)s2/χ2L)=		11.984

from above 90% confidence interval for population standard deviation =(4.319<σ<11.984)