Mathematical Statistics

One thing the manager is interested in is determining if the time between arrivals has gotten smaller on average. If this can be confirmed to likely be the case, she may recommend to the board that another drive-up lane be added. In particular, she wants to determine if the average of the successive arrival times is less than 5 minutes.

Suppose that a random sample of n successive arrival times will be taken, determine the form of the Uniformly Most Powerful test for testing:

H_o: θ ≥θ_o

H_a: θ<θ_o