The natural radiation has an average lambda2 per unit time T

The natural radiation has an average lambda=2 (per unit time). They decide to do a test Let X1,..,Xs be independently Poisson distributed with parameter lambda. We USC significance level alpha=0.0487. Device the most powerful test or deciding between the two hypotheses on basis of these five measurements. Determine the Critical Region. What is the power of this test? Determine the p-value of the optimal test based on these data. Explain clearly please.

Solution

As nothing is mentioned about the type of test. Goodness of fit for Poission distribution can be worked out. Kindly let me know as the test details are missing.

Here I am confused why level of significance considered is 0.0487