The number of work-related injuries per week that occur at the manufacturing plant of the Excelsior Cor poration is a Poisson-distributed random variable with mean >.. 3, according to company analysts. In an at tempt to lower insurance costs, the corporation insti tutes a program of intensive safety instruction for all employees. Upon completion of the program, a 12-week period produced an average of 2 accidents per week.
a. Design a uniformly most powerful level-.10 test of the null hypothesis H0 : >.. 3 versus the alterna tive hypothesis Ha : >.. <>3 having size as close as possible to, 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?