Question

Question Help The values isted below are waiting times in minutes of customers at two different banks At Bark A customers are a single wasting in foods three die windows At Bank B, customers may be any one of three different lines that have formed at the windows. Answer the fingers Bank A 65 67 Bank B 7.1 7.7 54 62 25 100 Click the icon to view the table of Ch Square critical values Construct a confidence interval for the population standard deviation at Bank minow*** (Round to two decimal places as needed) Construct a confidence interval for the population standard deviation Bank (Round to two decimal places as needed

Answer 1

BANK  A

Sample Size,   n=   10
Sample Standard Deviation,   s=   0.4835
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    9
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   2.700
Upper Chi-Square Value=   χ²α/2 =   19.023

confidence interval for std dev is       
lower bound= √[(n-1)s²/χ²α/2] =   √(9*0.4835² / 19.0228)=   0.3326
      
      
upper bound= √[(n-1)s²/χ²1-α/2] =   √(9*0.4835² / 2.7004)=   0.8827
      
CI ( 0.33 , 0.88)

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BANK B

Sample Size,   n=   10
Sample Standard Deviation,   s=   1.8301
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    9
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   2.700
Upper Chi-Square Value=   χ²α/2 =   19.023

confidence interval for std dev is       
lower bound= √[(n-1)s²/χ²α/2] =   √(9*1.8301² / 19.0228)=   1.2588
      
      
upper bound= √[(n-1)s²/χ²1-α/2] =   √(9*1.8301² / 2.7004)=   3.3411
      
CI (1.25 , 3.34)

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OC. The variation appears to be significantly lower with a single line system. The single-line system appears to be better

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Please let me know in case of any doubt.

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