Question

1. A bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce the waiting time that currently is 10 minutes.

1. Formulate the hypotheses and rejection rule for this problem.

2. A random sample of 70 waiting times was obtained after the system was implemented. The sample showed a sample mean of 9.5 minutes and a standard deviation of 2.2 minutes. Obtain the p-value.

3. At alpha=.01, do you believe the new system indeed reduced the waiting time? Explain.

Answer 1

Ho :   µ =   10                  
Ha :   µ <   10       (Left tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s =    2.2000                  
Sample Size ,   n =    70                  
Sample Mean,    x̅ =   9.5000                  
                          
degree of freedom=   DF=n-1=   69                  
                          
Standard Error , SE = s/√n =   2.2000   / √    70   =   0.2630      
t-test statistic= (x̅ - µ )/SE = (   9.500   -   10   ) /    0.2630   =   -1.90
                                
                          
p-Value   =   0.0307   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis

There is not sufficient evidence to prove that new system indeed reduced the waiting time .

Please revert back in case of any doubt.

Please upvote. Thanks in advance.