Question

A supermarket buys oranges from a certain company, that claims that the fraction of unacceptable fruit (e.g., rotten) in each shipment does not exceed 3%. The supermarket is willing to accept such (but not higher) percentage of bad fruit. The procedure agreed upon specifies that a random sample of 30 oranges will be selected from each shipment (the method of sampling is typically also a part of the protocol). The shipment will be accepted if there is no more than one unacceptable fruit in this sample, and rejected (or bought at a discounted price, etc.) otherwise. Compute and interpret the size of the test and the power function.

Answer 1

The critical region le is nothing but the values of szó, that leads to the rejection of the null hypothesir te the rejection of the supplier's claim that 0 6 Oo Now, the power function of this test is , ad ITCO) Po { $307, 23 min sit wat Go Go El st = 1 - Po {$30 = 0) Po { S30 = 1}