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© 2010 Pearson Prentice Hall. All rights reserved Hypothesis Testing Basics

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10-2 A hypothesis is a statement regarding a characteristic of one or more populations.

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10-3 The null hypothesis, denoted H 0, is a statement to be tested. The null hypothesis is a statement of no change, no effect or no difference. The null hypothesis is assumed true until evidence indicates otherwise.

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10-4 The alternative hypothesis, denoted H 1, is a statement that is to the contrary of the null hypothesis. In a standard hypothesis testing process this is the statement we are trying to find evidence to support.

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10-5 There are three basic ways to set up the null and alternative hypotheses: 1.Equal versus not equal hypothesis (two-tailed test) H 0 : parameter = some value H 1 : parameter ≠ some value

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10-6 There are three basic ways to set up the null and alternative hypotheses: 1.Equal versus not equal hypothesis (two-tailed test) H 0 : parameter = some value H 1 : parameter ≠ some value 2.Equal versus less than (left-tailed test) H 0 : parameter = some value H 1 : parameter < some value

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10-7 There are three basic ways to set up the null and alternative hypotheses: 1.Equal versus not equal hypothesis (two-tailed test) H 0 : parameter = some value H 1 : parameter ≠ some value 2.Equal versus less than (left-tailed test) H 0 : parameter = some value H 1 : parameter < some value 3.Equal versus greater than (right-tailed test) H 0 : parameter = some value H 1 : parameter > some value

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10-8 “In Other Words” The null hypothesis is a statement of “status quo” or “no difference” and always contains a statement of equality. The null hypothesis is assumed to be true until we have evidence to the contrary. The claim that we are trying to gather evidence for determines the alternative hypothesis.

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10-9 For each of the following claims, determine the null and alternative hypotheses. State whether the test is two-tailed, left-tailed or right-tailed. a)In 2008, 62% of American adults regularly volunteered their time for charity work. A researcher believes that this percentage is different today. b)According to a study published in March, 2006 the mean length of a phone call on a cellular telephone was 3.25 minutes. A researcher believes that the mean length of a call has increased since then. c)Using an old manufacturing process, the standard deviation of the amount of wine put in a bottle was 0.23 ounces. With new equipment, the quality control manager believes the standard deviation has decreased. Parallel Example : Forming Hypotheses

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10-10 a)In 2008, 62% of American adults regularly volunteered their time for charity work. A researcher believes that this percentage is different today. The hypothesis deals with a population proportion, p. If the percentage participating in charity work is no different than in 2008, it will be 0.62 so the null hypothesis is H 0 : p=0.62. Since the researcher believes that the percentage is different today, the alternative hypothesis is a two-tailed hypothesis: H 1 : p≠0.62. Solution

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10-11 b)According to a study published in March, 2006 the mean length of a phone call on a cellular telephone was 3.25 minutes. A researcher believes that the mean length of a call has increased since then. The hypothesis deals with a population mean, . If the mean call length on a cellular phone is no different than in 2006, it will be 3.25 minutes so the null hypothesis is H 0 : =3.25. Since the researcher believes that the mean call length has increased, the alternative hypothesis is: H 1 : > 3.25, a right-tailed test. Solution

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10-12 1.We reject the null hypothesis when the alternative hypothesis is true. This decision would be correct. Four Outcomes from Hypothesis Testing

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10-13 1.We reject the null hypothesis when the alternative hypothesis is true. This decision would be correct. 2.We do not reject the null hypothesis when the null hypothesis is true. This decision would be correct. Four Outcomes from Hypothesis Testing

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10-14 1.We reject the null hypothesis when the alternative hypothesis is true. This decision would be correct. 2.We do not reject the null hypothesis when the null hypothesis is true. This decision would be correct. 3.We reject the null hypothesis when the null hypothesis is true. This decision would be incorrect. This type of error is called a Type I error. Four Outcomes from Hypothesis Testing

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10-15 1.We reject the null hypothesis when the alternative hypothesis is true. This decision would be correct. 2.We do not reject the null hypothesis when the null hypothesis is true. This decision would be correct. 3.We reject the null hypothesis when the null hypothesis is true. This decision would be incorrect. This type of error is called a Type I error. 4.We do not reject the null hypothesis when the alternative hypothesis is true. This decision would be incorrect. This type of error is called a Type II error. Four Outcomes from Hypothesis Testing

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Hypothesis Testing Error Table H 0 is trueH 0 is false We reject H 0 Type I error committed, α No error committed We Fail to reject H 0 No error committedType II error committed, β

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10-17 The probability of making a Type I error, , is chosen by the researcher before the sample data is collected. The level of significance, , is the probability of making a Type I error.

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10-18 As the probability of a Type I error increases, the probability of a Type II error decreases, and vice-versa.

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10-19 CAUTION! We never “accept” the null hypothesis because without having access to the entire population, we don’t know the exact value of the parameter stated in the null. Rather, we say that we do not reject the null hypothesis. This is just like the court system. We never declare a defendant “innocent”, but rather say the defendant is “not guilty”.

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