Question

Scores on an IQ test are normally distributed. A sample of 10 IQ scores had standard deviation s=7. (a) Construct a 98% confidence interval for the population standard deviation . Round the answers to at least two decimal places. (b) The developer of the test claims that the population standard deviation is 9. Does this confidence interval contradict this claim? Explain  

Answer 1

a(

	here n =	10
	s2=7^2=	49.000
Critical value of chi square distribution for n-1=9 df and 98 % CI
Lower critical value χ2L=		2.088
Upper critical valueχ2U=		21.666

for Confidence interval of standard deviation:
Lower bound =√((n-1)s2/χ2U)=(10-1)*49/21.686=		4.512
Upper bound =√((n-1)s2/χ2L)=(10-1)*49/2.088 =		14.533
from above 98% confidence interval for population standard deviation =(4.512<σ<14.533)

b)

since 9 does fall between interval values of confidence interval, claim made by  developer is plausible.