823 THE BANK CUSTOMER WAITING TIME CASE The mean and the sta

8.23 THE BANK CUSTOMER WAITING TIME CASE The mean and the standard deviation of the sample of 100 bank customer waiting times in Table 1.8 are 5.46 and 2.475, respectively. Calculate a t - based 95 percent confidence interval for mu, the mean of all possible bank customer waiting times using the new system. Are we 95 percent confident that mu is less than six minutes?

Solution

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
              
X = sample mean =    5.46          
t(alpha/2) = critical t for the confidence interval =    1.984216952          
s = sample standard deviation =    2.475          
n = sample size =    100          
df = n - 1 =    99          
Thus,              
              
Lower bound =    4.968906304          
Upper bound =    5.951093696          
              
Thus, the confidence interval is              
              
(   4.968906304   ,   5.951093696   )

As the upper bound is less than 6, then YES, we are 95% confident that u is less than 6 minutes.