The values listed below are waiting times (in minutes) of customers at two diffe
ID: 3131457 • Letter: T
Question
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
7.67.6
7.97.9
7.97.9
7.97.9
Bank Upper BBank B
4.24.2
5.55.5
5.85.8
6.36.3
6.66.6
7.77.7
7.77.7
8.58.5
9.29.2
10.010.0
Construct a 90% confidence interval for the population standard deviation at Bank A.
__ min< bank A< __min
__< bank B< __
Bank A
6.36.3
6.66.6
6.76.7
6.86.8
7.17.1
7.37.3
7.67.6
7.97.9
7.97.9
7.97.9
Bank Upper BBank B
4.24.2
5.55.5
5.85.8
6.36.3
6.66.6
7.77.7
7.77.7
8.58.5
9.29.2
10.010.0
Explanation / Answer
a)
Using the sample standard deviation for bank A,
s = 0.598980616
As
df = n - 1 = 9
alpha = (1 - confidence level)/2 = 0.05
Then the critical values for chi^2 are
chi^2(alpha/2) = 16.9189776
chi^2(alpha/2) = 3.325112843
Thus, as
lower bound = (n - 1) s^2 / chi^2(alpha/2) = 0.190850776
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) = 0.971094864
Thus, the confidence interval for the variance is
( 0.190850776 , 0.971094864 )
Also, for the standard deviation, getting the square root of the bounds,
( 0.436864711 , 0.985441457 ) [ANSWER]
*********************
b)
Using the sample standard deviation for bank B,
s = 1.7958285
As
df = n - 1 = 9
alpha = (1 - confidence level)/2 = 0.05
Then the critical values for chi^2 are
chi^2(alpha/2) = 16.9189776
chi^2(alpha/2) = 3.325112843
Thus, as
lower bound = (n - 1) s^2 / chi^2(alpha/2) = 1.715529194
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) = 8.729027068
Thus, the confidence interval for the variance is
( 1.715529194 , 8.729027068 )
Also, for the standard deviation, getting the square root of the bounds,
( 1.309782117 , 2.954492692 ) [ANSWER]
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