chapter 8 b - Chapter 8.4: Testing hypotheses about a...

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1 Example 1 .Suppose that a pharmaceutical company is concerned that the mean potency µ of an antibiotic does not meet the minimum government potency standards. They need to decide between two possibilities: The mean potency µ does not exceed the mean allowable potency. The mean potency µ exceeds the mean allowable potency. Chapter 8.4: Testing hypotheses about a population mean m (large samples). Example 2 . In trying a person for a crime, the jury needs to decide between one of two possibilities: The person is guilty. The person is innocent. • To begin with, the person is assumed innocent. • The prosecutor presents evidence, trying to convince the jury to reject the original assumption of innocence, and conclude that the person is guilty. Main steps in testing statistical hypotheses. 1.Formulate the null hypothesis and the research (alternative) hypothesis. The null hypothesis, H 0 :status quo, present state. Assumed to be true until we can prove otherwise. The alternative hypothesis, H 1 : it is called research, because it implies that some action is to be performed. We do not prove H 0 rather look for evidence to support H 1. Court trial: Pharmaceuticals: H 0 : innocent H 0 : µ does not exceed allowed amount H 1 : guilty H 1 : µ exceeds allowed amount Types of Hypotheses: Two-Tailed Tests Example 3: Is it true that the average hourly wage of construction workers in California is different from $14, which is the national average? – Answering this question is equivalent to testing the hypothesis : H 0 : µ =14 against H 1 : µ≠ 14 where µ is the average hourly wage of construction workers in the USA. This is an example of a two-tailed test of hypotheses. directions of H 1 µ =14 µ> 14 µ< 14
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2 Types of Hypotheses: The one-tailed test Example 4: The average duration of Alzheimer’s disease from the onset of symptoms until death is 8 years. A pharmaceutical company claims to have developed a new drug which increases the expected lifetime. – Verifying the company’s claim would be equivalent to testing: H 0 : µ =8 against H 1 : µ >8 where µ is the average duration of the disease (i.e. average time before death). This is an example of the
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chapter 8 b - Chapter 8.4: Testing hypotheses about a...

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