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Testing Hypotheses About Proportions

Testing Hypotheses About Proportions - STAT E-50...

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STAT E-50 - Introduction to Statistics Testing Hypotheses About Proportions Hypotheses The null hypothesis: H 0 : parameter = hypothesized value The alternative hypothesis: H a : parameter = value we would accept if we reject the null hypothesis Model Specify the model you will use to test the null hypothesis State the parameter of interest List the assumptions and check the conditions Name the statistical test you will use Mechanics Calculate a test statistic from the data Obtain a P-value = the probability that the observed value of the test statistic (or a more extreme value) could occur if the null model were correct If the P-value is small enough, we will reject the null hypothesis Conclusion Statistical conclusion: state whether you reject or fail to reject the null hypothesis State your conclusion in context
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One-proportion z-test H 0 : p = p 0 Test statistic is 0 ˆ p p z ˆ SD(p) = where 0 0 p q ˆ SD (p) n = When the conditions are met and the null hypothesis is true, this statistic follows the standard Normal model. Conditions: Independence condition Random sampling condition 10% condition Success/failure condition (using p 0 and q 0 ) Note: p 0 is the value you are testing in H 0 ; q 0 = 1 - p 0 is the observed value of p ˆ p Page 2
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1. An American Demographics study conducted in 1980 found that 40% of new car buyers were women. Suppose that in a random sample of 120 new car buyers in 2000, 57 were women. Does this indicate that the true proportion of new car buyers in 2000 who were women is significantly larger than the 1980 proportion? Plan What do we want to know? What are the variables? What are the W’s? Hypotheses H 0 : H a : Model Check the conditions: Independence condition Random sampling condition 10% condition Success/failure condition (using p 0 and q 0 ) Specify the sampling distribution model What test do you plan to use?
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