A bank branch located in a commercial district of a city has

A bank branch located in a commercial district of a city has the business objective of improving the process for serving customers during lunch hour. THE WAITING TIME FOR OF A RANDOM SAMPLE OF 36 CUSTOMERS IS COLLECTED, AND THE RESULTS (IN MINUTES) ARE SUMMARIZED AS FOLLOWS: X=4 MINUTES; S=1.5 MINUTES. cAN WE CONCLUDE THAT THE MEAN WAITING TIME IS NOW BELOW 5 MINUTES? uSE A SIGNAFICANCE LEVEL OF 0.05

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   5  
Ha:    u   <   5  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical z, as alpha =    0.05   ,      
alpha =    0.05          
zcrit =    -   1.644853627      
              
Getting the test statistic, as              
              
X = sample mean =    4          
uo = hypothesized mean =    5          
n = sample size =    36          
s = standard deviation =    1.5          
              
Thus, z = (X - uo) * sqrt(n) / s =    -4          
              
Also, the p value is              
              
p =    3.16712*10^-5          
              
As |z| < 1.6449, and P < 0.05, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the mean waiting time is now below 5 minutes. [CONCLUSION]