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Intro Stats Week 9

The confidence interval is phat z x sep hat where the

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Unformatted text preview: umption When the conditions are met, we are ready to find the confidence interval for the population proportion, p. The confidence interval is phat +/- z* x SE(p-hat), where the standard deviation of the proportion is estimated by SE (p-hat) = rad(p-hat*q-hat/n) Don’t suggest that the parameter varies Don’t claim that other samples will agree with yours Don’t be certain about the parameter Don’t forget: It’s about the parameter Don’t claim to know too much Do take responsibility Do treat the whole interval equally ◦ Success/failure condition: We must expect at least 10 “successes” and 10 “failures” 4 10/30/2011 The null hypothesis which we denote H0, hypothesis, specifies a population model parameter of interest and proposes a value for that parameter Testing Hypothesis About Proportions ◦ H0: parameter=hypothesized value The alternative hypothesis which we denote hypothesis, HA, contains the values of the parameter which we consider plausible if we reject the null hypothesis ◦ HA: parameter greater than, less then or simply not equal to the hypothesized value Innocent until proven guilty ◦ Being innocent the null hypothesis Have to be proven guilty beyond a reasonable doubt ◦ Look at the p-value If guilty, guilty beyond a reasonable doubt ◦ High enough -value Otherwise, not guilty. Never proven innocent! ◦ We never prove the null hypothesis true; rather, we fail to reject it 1. 2. 3. 4. Hypothesis Model Mechanics Conclusion We want to find the probability of seeing data like this given the null hypothesis is true ◦ This probability is the P-value Never Never accept the null hypothesis! In computing a hypothesis test, we are looking at the evidence to see if there the probability of the null being “innocent” is so low that it can’t possibly be true. Otherwise, we concede it might be true First we state the null hypothesis ◦ ◦ ◦ ◦ Usually the skeptical claim that nothing’s different Saying “oh yeah? Convince me?” Have to pile up evidence to reject it H0: parameter = hypothesized value The alternative hypothesis, HA , contains the values of the parameter plausible when we reject the null The arriagnment 5 10/30/2011 Specify the model you will use to test the null hypothesis and the parameter of interest Different courts have different jurisdictions! The test about proportions is called a oneoneproportion z-test zCheck assumptions and conditions for using model Actual calculation of our test statistic Ultimate goal of the calculation is to obtain a p-value The trial The conclusion in a hypothesis test is always a statement about the null hypothesis The verdict The conclusion must state either that we reject or that we fail to reject the null hypothesis. And, it must be stated in context The effect size matters! The conditions for the one-proportion z-test are the same as for the one-proportion zinterval. We test the hypothesis H0: p=p0 using the statistic z= (p-hat-p0 / SD(p-hat)). We use the hypothesized proportion to find the standard deviation, SD (p-hat) = rad(p0q0/n). When the conditions are met and the null hypothesis is true, this statistic follows the standard Normal model, so we can use that model to obtain a P-value ◦ Think of confidence intervals! Questions? Remember, Second Article due today! 6...
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