Hypothesis of Testing 1 Notes Spring

Hypothesis of Testing 1 Notes Spring - 2 of 14 1.1...

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Unformatted text preview: 2 of 14 1.1 Introduction Question 1 . How could you support your claim? Question 2 . You conduct a study of our class and find the proportion of stu- dents who wear corrective lenses is 55.6%. Does this support our hypothesis that the proportion of people in the US who wear corrective lenses is less than 56 percent? Why? Question 3 . What would we need to know to support our hypothesis that the proportion of people in the US who wear corrective lenses is less than 56 percent? Goal • Find probability of observing a sample proportion at least as extreme as ˆ p = 0 . 556. • If we can determine that it is unlikely to observe ˆ p = 0 . 556 assuming p = 0 . 56 then the rare event rule would make us question our assumption that p = 0 . 56 and allow us to support our claim that p < . 56. Sampling distribution of ˆ p If np and nq ≥ 5 then p will have a normal distribution 2 and the CLT tells us that ˆ p is approximately normally distribution where: μ ˆ p = p (1) σ ˆ p = r pq n (2) Probability of observing our sample data. In our case p = 0 . 56, n = 18. We want to find the probability of observing a sample proportion at least as extreme as 0.556: P (ˆ p < . 556). 2 Normal approximation of binomial. Anthony Tanbakuchi MAT167 Introduction to Hypothesis Testing 3 of 14 0.0 0.2 0.4 0.6 0.8 1.0 0.0 1.0 2.0 3.0 Sampling distribution of p p ^ The above plot is the sampling distribution for ˆ p assuming μ ˆ p = p = 0 . 56 and the shaded area . 5 . Since p-value = 0 . 5: Question 4 . Using the rare event rule, would it be unusual to observe a sample proportion at least as extreme as 0 . 556 if the true population value is 0 . 56? Question 5 . Can we support our claim that the proportion of people in the US who wear corrective lenses is less than 56 percent? Question 6 . If we decided to support our claim that the proportion of people in the US who wear corrective lenses is less than 56 percent, what is the probability that we made the wrong decision? In other words, what is the probability that we would observe ˆ p = 0 . 556 from a random sample drawn from a population with p = 0 . 56 Question 7 . Under what conditions can we support our claim via the rare event rule?...
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Hypothesis of Testing 1 Notes Spring - 2 of 14 1.1...

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