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Unformatted text preview: CHAPTER 4: PROBABILITY & PROBABILITY DISTRIBUTIONS 4.1 HOW PROBABILITY CAN BE USED IN MAKING INFERENCES We stated in Chapter 1 that a scientist uses inferential statistics to make statements about a population based on information contained in a sample. Because such statements or decisions are made under conditions of uncertainty, the use of probability concepts is required. Probability concepts help us make better decisions in the face of uncertainty, and allow us to assess the likelihood of an event happening. Graphical and numerical descriptive techniques were presented in Chapter 3 as a means to summarize and describe a sample. However, a sample is not identical to the population from which it was selected. We need to assess the degree of accuracy to which the sample mean, sample standard deviation, or sample proportion represent the corresponding population values. Suppose a company states in its promotional materials that its pregnancy test provides correct results in 75% of its applications by pregnant women. We want to evaluate the claim, and so we select 20 women who have been determined by their physicians, using the best possible testing procedures, to be pregnant. The test is taken by each of the 20 women. For all of these 20 women the test result is negative, indicating that none of the 20 women is pregnant. What do you conclude about the company’s claim on the reliability of its test? Suppose you are further assured that each of the 20 women was in fact pregnant, as was determined several months after the test was taken. At what point do we decide that the result of the observed sample is so improbable, assuming the company’s claim is correct, that we disagree with its claim? To answer this question, we must know how to find the probability of obtaining a particular sample outcome. Knowing this probability, we can then determine whether we agree or disagree with the company’s claim. Probability is the tool that enables us to make inference. In other words, probability is the basis of inferential statistics . For example, predictions are based on probability, and hypotheses are tested by using probability. Dr. LOHAKA –QBA 2302 Chapter 4: PROBABILITY & PROBABILITY DISTRIBUTIONS Page 129 4.2 PROBABILITY, PROBABILITY EXPERIMENT, SAMPLE SPACE, EVENT, and PROBABILITY OF AN EVENT DEFINITION 4.1: PROBABILITY Probability is a value between zero and one , inclusive , describing the relative possibility (chance or likelihood) that something will happen. In practical terms, the probability of any thing is a number between and 1 that describes the long-run proportion of the time that thing occurs when the experiment is performed repeatedly under identical conditions....
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- Spring '08
- Probability, Probability theory, Probability Distributions Page, Dr. LOHAKA, Dr. LOHAKA QBA