8.1-8.2_1_

8.1-8.2_1_ - (8.1,8.2 The sampling distribution of a sample...

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Inference for proportions (8.1, 8.2)
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Sampling distribution of       —  reminder  The sampling distribution of a sample proportion is approximately normal (normal approximation of a binomial distribution) when the sample size is large enough. p ˆ
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Conditions for inference on  p Assumptions: 1. The data used for the estimate are an SRS from the population studied. 2. The population is at least 20 times as large as the sample used for inference. This ensures that the standard deviation of is close to under without-replacement sampling. 3. The sample size n is large enough that the sampling distribution can be approximated by a normal distribution. How large a sample size is required depends in part on the value of p . Otherwise, use the binomial distribution. p (1 - p ) n
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Large-sample confidence intervals for  p Use this method when the number of successes and the number of failures are both at least 15. C Z * Z * m m For an SRS of size n drawn from a large population and with sample proportion calculated from the data, an approximate level C confidence interval for p is: n p p z SE z m m m p ) ˆ 1 ( ˆ * * error of margin the is , ˆ - = = ±
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Medication side effects Arthritis is a painful, chronic inflammation of the joints. An experiment on the side effects of pain relievers examined arthritis patients to find the proportion of patients who suffer side effects.
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effects. Let’s calculate a 90% confidence interval for the population proportion of arthritis patients who suffer side effects. 023 . 0 014 . 0 * 645 . 1 440 / ) 052 . 0 1 ( 052 . 0 * 645 . 1 ) ˆ 1 ( ˆ * = - = - = m m n p p z m 052 . 0 440 23 ˆ = p For a 90% confidence level, z * = 1.645. Using the large sample method, we calculate a margin of error m : With 90% confidence level, between 2.9% and 7.5% of arthritis patients taking this pain medication experience some adverse symptoms. 023
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8.1-8.2_1_ - (8.1,8.2 The sampling distribution of a sample...

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