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# 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.
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
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
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
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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