Question

3. A radiation detector is used to measure the danger to humans working in a particular room. For illustration, we will model X = the number of radioactive "clicks” registered in a standard time period as a Poisson with mean . That is to say, P(X = k) = for k = 0,1,2,... Presume that 1 = 2 is “safe” but larger means (indicating higher radiation levels) are not. Suppose that one determines to declare that there is an unsafe radiation level if X > 3.

1. What is the type I error probability for this approach? (PLUG-IN completely, NO need to simplify.)

2. What is the type II error probability if in fact the radiation level(λ) is twice the maximum safe level? (PLUG-IN completely, NO need to simplify.)

3. What p-value for a test of H0: λ=2 is associated with an observation X = 4? (PLUG-IN completely, NO need to simplify.)

Answer 1

Answe Hoc Ho d22 Ng Hiid> and P(x-2). Eddk Koolie, - KI 4) P[type - Tenor) ff xya) x=3 1- 0.6767.323 3 pltype - I exror) - Placcepto. 4) 0.7619 c) P-value - P/X24 |d: 2) - 0.1429