Question

The waiting times​ (in minutes) of a random sample of

2020

people at a bank have a sample standard deviation of

4.64.6

minutes. Construct a confidence interval for the population variance

sigma squaredσ2

and the population standard deviation

sigmaσ.

Use a

95 %95%

level of confidence. Assume the sample is from a normally distributed population.

What is the confidence interval for the population variance

sigma squaredσ2​?

​(nothing​,nothing​)

​(Round to one decimal place as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to one decimal place as​ needed.)

A.

With

95 %95%

​confidence, you can say that the population variance is

greatergreater

than

nothing.

B.

With

95 %95%

​confidence, you can say that the population variance is between

nothing

and

nothing.

C.

With

55​%

​confidence, you can say that the population variance is

lessless

than

nothing.

D.

With

55​%

​confidence, you can say that the population variance is between

nothing

and

nothing.

What is the confidence interval for the population standard deviation

sigmaσ​?

​(nothing​,nothing​)

​ (Round to one decimal place as​ needed.)

Interpret the results. Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to one decimal place as​ needed.)

A.

With

55​%

​confidence, you can say that the population standard deviation is

greatergreater

than

nothing

minutes.

B.

With

9595​%

​confidence, you can say that the population standard deviation is

lessless

than

nothing

minutes.

C.

With

55​%

​confidence, you can say that the population standard deviation is between

nothing

minutes and

nothing

minutes.

D.

With

9595​%

​confidence, you can say that the population standard deviation is between

nothing

and

nothing

minutes.

Answer 1

s = 4.6 , n = 20

alpha = 0.05

chi square value for lower bound = 32.8523
chi square value for upper bound = 8.9065

(20-1) 84.6^2/ 32.8523 < sigma^2 < (20-1) 84.6^2/ 8.9065

12.2 < sigma^2 < 45.1

sqrt(12.2) < sigma < sqrt(45.1)

3.5 < sigma < 6.7

CI for population variance= ( 12.2 , 45.1)

With 95% ​confidence, you can say that the population variance is between 12.2 and 45.1

CI for std.deviation = (3.5 , 6.7)

With 95​% confidence, you can say that the population standard deviation is between 3.5 and 6.7