A retail store has six checkout counters and customers form separate lines at each counter. This setup has been in use for the last ten years and historical data indicates that the standard deviation of waiting time for customers is 7.5 minutes. It experimented with an alternate setup where customers form one line, from which they get directed to the next checkout counter that becomes free. A random sample of 25 customers showed a sample standard of waiting time to be 3.5 minutes. At a 1% level of significance can we conclude that the new setup has reduced the standard deviation of waiting times?

Question

A retail store has six checkout counters and customers form separate lines at each counter. This setup has been in use for the last ten years and historical data indicates that the standard deviation of waiting time for customers is 7.5 minutes. It experimented with an alternate setup where customers form one line, from which they get directed to the next checkout counter that becomes free. A random sample of 25 customers showed a sample standard of waiting time to be 3.5 minutes. At a 1% level of significance can we conclude that the new setup has reduced the standard deviation of waiting times?

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