A shipment of 20 projection screen television sets is at the receiving dock of a large department store. The de partment store has a policy of not accepting shipments that contain more than 10 percent defective merchan dise. The receiving clerk is instructed to have a quality inspection done on two sets that are randomly drawn, without replacement, from the shipment. Letting k rep resent the unknown number of defective sets in the shipment of 20 sets, the null hypothesis Ho : k ::::: 2 will be rejected iff both sets that are inspected are found to be defective.
a. Calculate the probabilities of committing type I er rors when k = 0, l, or 2.
b. Calculate the probabilities of committing type II errors when k 23.
c. Plot the power function of this testing procedure. Interpret the implications of the power function from the standpoint of both the department store and the television manufacturer.