Question

In: Statistics and Probability

The values listed below are waiting times​ (in minutes) of customers at two different banks. At...

The values listed below are waiting times​ (in minutes) of customers at two different banks. At Bank​ A, customers enter a single waiting line that feeds three teller windows. At Bank​ B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions.

Bank A

6.46.4

6.66.6

6.76.7

6.86.8

7.17.1

7.37.3

7.47.4

7.97.9

7.97.9

7.97.9

Bank B

4.14.1

5.35.3

5.85.8

6.26.2

6.66.6

7.87.8

7.87.8

8.48.4

9.39.3

10.010.0

Construct a 99​% confidence interval for the population standard deviation

sigma at Bank A.

_min < σ Bank A < _min

Construct a 99​% confidence interval for the population standard deviation

sigma at Bank B.

_min < σ Bank B < _min

Solutions

Expert Solution

Bank A ( X ) Σ ( Xi- X̅ )2 Bank B ( Y ) Σ ( Yi- Y̅ )2
6.4 0.64 4.1 9.1809
6.6 0.36 5.3 3.3489
6.7 0.25 5.8 1.7689
6.8 0.16 6.2 0.8649
7.1 0.01 6.6 0.2809
7.3 0.01 7.8 0.4489
7.4 0.04 7.8 0.4489
7.9 0.49 8.4 1.6129
7.9 0.49 9.3 4.7089
7.9 0.49 10 8.2369
Total 72 2.94 71.3 30.901

Mean X̅ = Σ Xi / n
X̅ = 72 / 10 = 7.2
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 2.94 / 10 -1 ) = 0.5715

Mean Y̅ = ΣYi / n
Y̅ = 71.3 / 10 = 7.13
Sample Standard deviation SY = √ ( (Yi - Y̅ )2 / n - 1 )
SY = √ ( 30.901 / 10 -1) = 1.853

For Bank A

S2 = 0.3266
α = 0.01
n = 10
((n-1)S2 / χ2 (0.01/2)) < σ2 < ((n-1)S2 / χ2 (1 - 0.01/2) )
(( 10-1 ) 0.3266 / χ2 (0.01/2) ) < σ2 < ((10-1)0.3266 / χ2 (1 - 0.01/2) )
χ2 (0.01/2) = 23.5894
χ2 (1 - 0.01/2) ) = 1.7349
Lower Limit = (( 10-1 ) 0.32662 / χ2 (0.01/2) ) = 0.1246
Upper Limit = (( 10-1 ) 0.32662 / χ2 (0.01/2) ) = 1.6943
99% Confidence interval is ( 0.1246 , 1.6943 )
( 0.1246 < σ2 < 1.6943 )
( 0.353 < σ < 1.3016 )

For Bank B

S2 = 3.4336
α = 0.01
n = 10
((n-1)S2 / χ2 (0.01/2)) < σ2 < ((n-1)S2 / χ2 (1 - 0.01/2) )
(( 10-1 ) 3.4336 / χ2 (0.01/2) ) < σ2 < ((10-1)3.4336 / χ2 (1 - 0.01/2) )
χ2 (0.01/2) = 23.5894
χ2 (1 - 0.01/2) ) = 1.7349
Lower Limit = (( 10-1 ) 3.43362 / χ2 (0.01/2) ) = 1.31
Upper Limit = (( 10-1 ) 3.43362 / χ2 (0.01/2) ) = 17.8122
99% Confidence interval is ( 1.31 , 17.8122 )
( 1.31 < σ2 < 17.8122 )
( 1.1446 < σ < 4.2205 )

orchestra answered 2 years ago
Next > < Previous

Related Solutions

The values listed below are waiting times? (in minutes) of customers at two different banks. At...
The values listed below are waiting times? (in minutes) of customers at two different banks. At Bank? A, customers enter a single waiting line that feeds three teller windows. At Bank? B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.36.3 6.66.6 6.76.7 6.86.8 7.17.1 7.37.3 7.47.4 7.87.8 7.87.8 7.87.8 Bank Upper BBank B 4.24.2 5.45.4 5.85.8 6.26.2 6.76.7 7.77.7 7.77.7 8.68.6 9.39.3 10.010.0 Construct aa...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At Bank​ A, customers enter a single waiting line that feeds three teller windows. At Bank​ B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.4 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 Bank B 4.1 5.3 5.9 6.2 6.8 7.6 7.6 8.4 9.4 10 Construct a 99​% confidence...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At Bank​ A, customers enter a single waiting line that feeds three teller windows. At Bank​ B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.46.4 6.66.6 6.76.7 6.86.8 7.17.1 7.27.2 7.57.5 7.87.8 7.87.8 7.87.8 Bank Upper BBank B 4.24.2 5.35.3 5.85.8 6.16.1 6.76.7 7.87.8 7.87.8 8.48.4 9.49.4 10.010.0 LOADING... Click...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At Bank​ A, customers enter a single waiting line that feeds three teller windows. At Bank​ B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.5 6.6 6.7 6.8 7.1 7.3 7.6 7.9 7.9 7.9 Bank Upper B 4.3 5.3 5.9 6.2 6.8 7.8 7.8 8.4 9.2 10.0 Construct a 95%...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At...
The values listed below are waiting times​ (in minutes) of customers at two different banks. At Bank​ A, customers enter a single waiting line that feeds three teller windows. At Bank​ B, customers may enter any one of three different lines that have formed at three teller windows. Answer the following questions. Bank A 6.5 6.6 6.7 6.8 7.1 7.2 7.5 7.9 7.9 7.9 Bank B 4.2 5.4 5.8 6.2 6.8 7.7 7.7 8.5 9.3 10.00 a) Using Chi-Square critical...
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting...
Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation. Bank A (single line): 6.5 6.6 6.7 6.9 7.1 7.3 7.4 7.6 7.7 7.8 Bank B (individual lines): 4.4 5.4 5.7 6.2 6.7 7.7 7.8 8.4 9.4 9.9 The...
Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting...
Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation. Bank A​ (single line): 6.6 nbsp 6.6 nbsp 6.7 nbsp 6.8 nbsp 7.0 nbsp 7.3 nbsp 7.5 nbsp 7.7 nbsp 7.7 nbsp 7.8 Bank B​ (individual lines): 4.4 nbsp...
Waiting times​ (in minutes) of customers in a bank where all customers enter a single waiting...
Waiting times​ (in minutes) of customers in a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the mean and median for each of the two​ samples, then compare the two sets of results. Single Line 6.5 6.6 6.7 6.8 7.0 7.1 7.5 7.6 7.6 7.6 Individual Lines 4.2 5.4 5.8 6.2 6.5 7.6 7.6 8.6 9.2 9.9 The mean waiting time...
Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting...
Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation. Bank A​ (single line): 6.5 6.6 6.7 6.8 7.1 7.4 7.4 7.6 7.7 7.8 Bank B​ (individual lines): 4.2 5.4 5.8 6.2 6.7 7.7   7.8 8.6 9.3 9.9 The coefficient...
14.Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting...
14.Waiting times​ (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of​ data, then compare the variation Bank A (single line) Bank B (individual lines) 6.4 4.3 6.5 5.5 6.6 5.9 6.8 6.3 7.1 6.7 7.4 7.6 7.4 7.8 7.7 8.4 7.7 9.4 7.8 9.7 The...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT