Question

8.27. The PNC bank manager of WMU branch 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 waiting times from the current nine to ten minutes to less than 6 minutes.Average waiting time was obtained as 5.46 based on a random sample of 25 waiting times. Is there enough evidence at the 5% level of significance to validate managers claim? Assume that the standard deviation of all waiting times during peak hours is 2.47.

Answer 1

H0: >= 6

Ha: < 6

Test Statistic :-           

Z = ( X - µ ) / ( σ / √(n))          

Z = ( 5.46 - 6 ) / ( 2.47 / √( 25 ))          

Z = -1.09          

Decision rule-

Reject null hypothesis if Z < -Z(α)          

From Z table,

Left tailed critical value at 0.05 level = -1.645          

Since test statistics > -1.645 , Fail to reject null hypothesis   

We conclude that we fail to support the claim that the new system will reduce waiting times

from the current nine to ten minutes to less than 6 minutes.