Under the null hypothesis Ho that traffic is typical, the

Chapter 11, Problem 11.7

(choose chapter or problem)

Under the null hypothesis Ho that traffic is typical, the number of call attempts in a 1-second interval (during rush hour) at a mobile telephone S\vitch is a Poisson random variable N \vith E[N] = 2.5. Over a T-second period, the measured call rate is NJ = (N1 + + N'r)/'1,, where N1, ... , N'r are iid Poisson random variables identical to N. However, \vhenever there is unusually heavy traffic (resulting from an accident or bad \Veather or some other event), the measured call rate M is higher than usual. Based on the observation M, design a significance test to reject the null hypothesis Ho that traffic is typical at a significance level ex= 0.05. Justify your choice of the rejection region R. Hint: You may use a Gaussian ( centra[ limit theorem) approximation for calculating probabilities \Vi th respect to M. Ho'v does your test depend on the observation period T? Explain your answer.