The values listed below are waiting times in minutes of cust

The values listed below are waiting times in minutes of customers. Customers enter one of three lines. Construct a confidence interval for the population standard deviation o and write a statement that interprets the results.

4.2    5.4   5.8   6.2   6.7   7.7   8.5   9.3   10.0  

Solution

Getting the standard deviation of the sample,

s = 1.92122646

If we assume a 95% confidence interval:

As              
              
df = n - 1 =    8          
alpha = (1 - confidence level)/2 =    0.025          
              
Then the critical values for chi^2 are              
              
chi^2(alpha/2) =    17.53454614          
chi^2(alpha/2) =    2.179730747          
              
Thus, as              
              
lower bound = (n - 1) s^2 / chi^2(alpha/2) =    1.684040673          
upper bound = (n - 1) s^2 / chi^2(1 - alpha/2) =    13.54703507          
              
Thus, the confidence interval for the variance is              
              
(   1.684040673   ,   13.54703507   )
              
Also, for the standard deviation, getting the square root of the bounds,              
              
(   1.297705927   ,   3.680629712   ) [ANSWER]

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Thus, we are 95% confident that the true population standard deviation is between 1.2977 and 3.6806. [ANSWER]