Question

As part of a​ survey, a marketing representative asks a random sample of 29 business owners how much they would be willing to pay for a website for their company. She finds that the sample standard deviation is ​$3288. Assume the sample is taken from a normally distributed population. Construct 95​% confidence intervals for​ (a) the population variance sigmasquared and​ (b) the population standard deviation sigma. Interpret the results. ​(a) The confidence interval for the population variance is ​( nothing​, nothing​). ​(Round to the nearest integer as​ needed.) Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to the nearest integer as​ needed.) A. With 5​% ​confidence, you can say that the population variance is less than nothing. B. With 5​% ​confidence, you can say that the population variance is between nothing and nothing. C. With 95​% ​confidence, you can say that the population variance is between nothing and nothing. D. With 95​% ​confidence, you can say that the population variance is greater than nothing. ​(b) The confidence interval for the population standard deviation is ​( nothing​, nothing​). ​(Round to the nearest integer as​ needed.) Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice. ​(Round to the nearest integer as​ needed.) A. With 95​% ​confidence, you can say that the population standard deviation is less than ​$ nothing. B. With 95​% ​confidence, you can say that the population standard deviation is between ​$ nothing and ​$ nothing. C. With 5​% ​confidence, you can say that the population standard deviation is greater than ​$ nothing. D. With 5​% ​confidence, you can say that the population standard deviation is between ​$ nothing and ​$ nothing.

Answer 1

a)

Critical value of chi square distribution for n-1=28 df and 95 % CI
Lower critical value χ2L=		15.308
Upper critical valueχ2U=		44.461

for Confidence interval of Variance:
Lower bound =(n-1)s2/χ2U=		6808358.61
Upper bound =(n-1)s2/χ2L=		19774394.56
from above 95% confidence interval for population variance =(6808359 <σ2< 19774395)

C. With 95​% ​confidence, you can say that the population variance is between 6808359 and 19774395

b)

Lower bound =√((n-1)s2/χ2U)=		2609.28
Upper bound =√((n-1)s2/χ2L)=		4446.84
from above 95% confidence interval for population standard deviation =(2609 <σ <4447)

B. With 95​% ​confidence, you can say that the population standard deviation is between 2609 and 4447