Standard +0.3 This is a straightforward hypothesis testing question requiring students to find a critical region for a one-tailed Poisson test. While it involves cumulative probability calculations and understanding of significance levels, it's a standard textbook procedure with no conceptual surprises—slightly easier than average since it's purely mechanical application of the critical region method.
It is thought that a random variable \(X\) has a Poisson distribution whose mean, \(\lambda\), is equal to 8.
Find the critical region to test the hypothesis \(H_0 : \lambda = 8\) against the hypothesis \(H_1 : \lambda < 8\),
working at the 1\% significance level. [5 marks]
It is thought that a random variable $X$ has a Poisson distribution whose mean, $\lambda$, is equal to 8.
Find the critical region to test the hypothesis $H_0 : \lambda = 8$ against the hypothesis $H_1 : \lambda < 8$,
working at the 1\% significance level. [5 marks]
\hfill \mbox{\textit{Edexcel S2 Q2 [5]}}