Question

The values listed below are waiting times in minutes) of customers at two different banks. Al Bank A customers enter a single waiting line that foods three teiler windows. Al Bank B, customers may enter any one of three differenties that have formed at three boller windows. Answer the following questions Bank A 66 6.7 58 7.1 72 7.5 Bank B 79 7.9 7.9 59 62 60 70 8.6 914 100 Click the icon to view the ble of Chi-Square critical values Construct a 95% confidence interval for the population standard deviation at Banka 0.40 m 105 min (Round to two decimal places as needed.) Construct a confidence trval for the population standard deviations at Bank (Round to two decimal places as needed)

Answer 1

a.
CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ᴪ^2 right < σ^2 < (n-1) s^2 / ᴪ^2 left
where,
s = standard deviation
ᴪ^2 right = (1 - confidence level)/2
ᴪ^2 left = 1 - ᴪ^2 right
n = sample size
since alpha =0.05
ᴪ^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
ᴪ^2 left = 1 - ᴪ^2 right = 1 - 0.025 = 0.975
the two critical values ᴪ^2 left, ᴪ^2 right at 9 df are 19.68 , 2.7
s.d( s )=0.5754
sample size(n)=10
confidence interval for σ^2= [ 9 * 0.33/19.68 < σ^2 < 9 * 0.33/2.7 ]
= [ 2.98/19.68 < σ^2 < 2.98/2.7 ]
[ 0.15 < σ^2 < 1.05 ]
and confidence interval for σ = sqrt(lower) < σ < sqrt(upper)
= [ sqrt (0.15) < σ < sqrt(1.05), ]
= [ 0.39 < σ < 1.02 ]
95% confidence interval for population standard deviation at Bank A
b.
CONFIDENCE INTERVAL FOR STANDARD DEVIATION
ci = (n-1) s^2 / ᴪ^2 right < σ^2 < (n-1) s^2 / ᴪ^2 left
where,
s = standard deviation
ᴪ^2 right = (1 - confidence level)/2
ᴪ^2 left = 1 - ᴪ^2 right
n = sample size
since alpha =0.05
ᴪ^2 right = (1 - confidence level)/2 = (1 - 0.95)/2 = 0.05/2 = 0.025
ᴪ^2 left = 1 - ᴪ^2 right = 1 - 0.025 = 0.975
the two critical values ᴪ^2 left, ᴪ^2 right at 9 df are 19.68 , 2.7
s.d( s )=1.8394
sample size(n)=10
confidence interval for σ^2= [ 9 * 3.38/19.68 < σ^2 < 9 * 3.38/2.7 ]
= [ 30.45/19.68 < σ^2 < 30.45/2.7 ]
[ 1.55 < σ^2 < 10.68 ]
and confidence interval for σ = sqrt(lower) < σ < sqrt(upper)
= [ sqrt (1.55) < σ < sqrt(10.68), ]
= [ 1.24 < σ < 3.27 ]
95% confidence interval for population standard deviation at Bank B