A surveillance camcra periodically checks a certain area

Chapter , Problem 30

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A surveillance camcra periodically checks a certain area and records a signal X = a" if there is no intruder (this is the null hypothesis Ho). If there is an intruder the signal is X = () + IV. where () is unknown with () > O. We assume that W is a normal random variable wit h mean 0 and known variance v = 0.5. (a) \\le obtain a single signal value X = 0.96. Should Ho be rejected at the 5% level of significance? (b) We obtain five independent signal values X = 0.96, -0.34, 0.85, 0.51, -0 . 24 . Should Ho be rejected at the 5% level of significance? (c) Repeat part (b). using the t-distribution, and assuming the variance v is unknown.

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