9. The number of work-related injuries per week that occur at the manufacturing plant of the Excelsior Corporation is a Poisson-distributed random variable with mean l  3, according to company analysts. In an attempt to lower insurance costs, the Corporation institutes a program of intensive safety instruction for all employees.

Upon completion of the program, a 12-week period produced an average of two accidents per week.

(a) Design a uniformly most powerful level .10 test of the null hypothesis H0: l  3 versus the alternative hypothesis Ha: l < 3 having size as close to .10 as possible without exceeding .10.

(b) Test the null hypothesis using the test you defined in part (a). What can you say about the effectiveness of the safety program?