Question

The average rate of emission radioactive particles from a source was measured over a long period, and found to be 10 particles per unit time. After an experimental treatment had been applied to the source, a further sample was examined and emitted 17 particles in unit time. Test at 5% the null hypothesis that the rate of emissions is unchanged.

Answer 1

Let

$$X\sim P_0(\lambda)$$

$H_0: \lambda=10$

$H_1: \lambda\not=10$

$$Pr(X\geq17)\approx0.02704>0.025=\alpha/2$$

The null hypothesis is accepted. There is insufficient evidence to reject $H_0.$

The rate of emissions is unchanged.