Question: A large retailer receives shipments of batteries for consumer electronic products in packages of 50 batteries. The packages are held at a distribution center and are shipped to retail stores as requested. Because some packages may contain defective batteries, the retailer randomly samples 400 packages from its distribution center and tests to determine whether the batteries are defective or not. The most recent sample of 400 packages revealed the following observed frequencies for defective batteries per package:

No. of defective batteries                  Frequency of
       per packages                            occurences

              0                                         165

              1                                         133

              2                                           65

              3                                           28

         4 or more                                      9

The retailer's managers would like to know if they can evaluate this sampling plan using a binomial distribution with n = 50 and p = 0.02. Test at the α = 0.01 level of significance.