TAILIEUCHUNG - Class Notes in Statistics and Econometrics Part 8

CHAPTER 15 Hypothesis Testing. Imagine you are a business person considering a major investment in order to launch a new product. The sales prospects of this product are not known with certainty. You have to rely on the outcome of n marketing surveys that measure the demand for the product once it is offered. | CHAPTER 15 Hypothesis Testing Imagine you are a business person considering a major investment in order to launch a new product. The sales prospects of this product are not known with certainty. You have to rely on the outcome of n marketing surveys that measure the demand for the product once it is offered. If p is the actual unknown rate of return on the investment each of these surveys here will be modeled as a random variable which has a Normal distribution with this mean p and known variance 1. Let y1 y2 . yn be the observed survey results. How would you decide whether to build the plant The intuitively reasonable thing to do is to go ahead with the investment if the sample mean of the observations is greater than a given value c and not to do 425 426 15. HYPOTHESIS TESTING it otherwise. This is indeed an optimal decision rule and we will discuss in what respect it is and how c should be picked. Your decision can be the wrong decision in two different ways either you decide to go ahead with the investment although there will be no demand for the product or you fail to invest although there would have been demand. There is no decision rule which eliminates both errors at once the first error would be minimized by the rule never to produce and the second by the rule always to produce. In order to determine the right tradeoff between these errors it is important to be aware of their asymmetry. The error to go ahead with production although there is no demand has potentially disastrous consequences loss of a lot of money while the other error may cause you to miss a profit opportunity but there is no actual loss involved and presumably you can find other opportunities to invest your money. To express this asymmetry the error with the potentially disastrous consequences is called error of type one and the other error of type two. The distinction between type one and type two errors can also be made in other cases. Locking up an innocent person is an error of type .

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