Week7[1] - 7 Chapter Week 7: Hypothesis Testing Click to...

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Click to edit Master subtitle style Chapter 7 Week 7: Hypothesis Testing
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Complementary Statements A Statistical Hypothesis Alternative hypothesis Ha contains a statement of inequality , such as <, or >. Null hypothesis H0 Statistical hypothesis that contains a statement of equality , such as , = or . If I am false, you are true If I am false, you are true H 0 H a A claim about a population.
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Write the claim about the population. Then, write its complement. Either hypothesis, the null or the alternative, can represent the claim. þ A hospital claims its ambulance response time is less than 10 minutes . H0 : 10 μ min Ha : 10 < min claim Ha : 60 . 0 p H0 : 60 . 0 p claim Writing Hypotheses þ A consumer magazine claims the proportion of cell phone calls made during evenings and weekends is at most 60%.
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A type I error: Null hypothesis is actually true but the decision is to reject it. Level of significance, α Maximum probability of committing a type I error. Decision Actual Truth of H0 Errors and Level of Significance H0 True H0 False Do not reject H0 Reject H0 Correct Decision Correct Decision Type II Error Type I Error
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Sampling distribution for x The rejection region is the range of values for which the null hypothesis is not probable . It is always in the direction of the alternative hypothesis. Its area is equal to α. Rejection Region 0 z z0 A critical value separates the rejection region from the non- rejection region Critical Value z0 Rejection Regions
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The critical value z0 separates the rejection region from the non- rejection region. The area of the rejection region is equal to α . z 0 0 Rejection region z 0 0 Rejection region - z0 0 z 0 Rejection region Rejection region Find z0 for a left-tail test with α =.01 Find z0 for a right-tail test with α =.05 Find - z0 and z0 for a two-tail test with α =.01 z0=-2.33 -z0=-2.575 and z0 =2.575 z0=1.645 Critical Values
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z 0 0 - z0 0 z 0 Right- tail test Ha: μ >value Reject H0 if z > z 0 otherwise fail to reject H0. Two- tail test Ha: μ value Reject H0 if z > z 0 or z <- z0 Left- tail test Ha: μ <value Reject H0 if z < z 0 otherwise fail to reject H0. Rejection region z 0 0 Rejection region Rejection region Rejection region Types of Hypothesis Tests
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Claim is H0 Reject H0 There is not enough evidence to reject the claim There is enough evidence to reject the claim Do not reject H0 Interpreting the Decision
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Claim is Ha Reject H0 There is not enough evidence to support the claim There is enough evidence to support the claim Do not reject H0 Interpreting the Decision
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1 . Write the null and alternative hypothesis 2 . State the level of significance 3 . Identify the sampling distribution Write H0 and Ha as mathematical statements. Remember H0 always contains the = symbol. This is the maximum probability of rejecting the null hypothesis when it is actually true. (Making a type I error.) The sampling distribution is the distribution for the test statistic assuming that H0 is true and that the experiment is repeated an infinite number of times.
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This note was uploaded on 05/17/2011 for the course BIS 115 taught by Professor Wright during the Spring '10 term at DeVry Chicago.

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Week7[1] - 7 Chapter Week 7: Hypothesis Testing Click to...

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