IPS6e.PPT.Ch08

# IPS6e.PPT.Ch08 - Inference for Proportions Inference for a...

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Inference for Proportions Inference for a Single Proportion IPS Chapter 8.1 © 2009 W.H. Freeman and Company

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Objectives (IPS Chapter 8.1) Inference for a single proportion Large-sample confidence interval for p “Plus four” confidence interval for p Significance test for a single proportion Choosing a sample size
Sampling distribution of sample proportion  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 10 times as large as the sample used for inference. This ensures that the standard deviation of is close to 3. The sample size n is large enough that the sampling distribution can be approximated with a normal distribution. How large a sample size is required depends in part on the value of p and the test conducted. Otherwise, rely on the binomial distribution. p (1 - p ) n p ˆ
Large-sample confidence interval 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 Confidence intervals contain the population proportion p in C % of samples. 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: C is the area under the standard normal curve between − z * and z *. n p p z SE z m m m p ) ˆ 1 ( ˆ * * error of margin the is , ˆ - = = ± p 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. What are some side effects of ibuprofen? Serious side effects (seek medical attention immediately): Allergic reaction (difficulty breathing, swelling, or hives), Muscle cramps, numbness, or tingling, Ulcers (open sores) in the mouth, Rapid weight gain (fluid retention), Seizures, Black, bloody, or tarry stools, Blood in your urine or vomit, Decreased hearing or ringing in the ears, Jaundice (yellowing of the skin or eyes), or Abdominal cramping, indigestion, or heartburn, Less serious side effects (discuss with your doctor): Dizziness or headache, Nausea, gaseousness, diarrhea, or constipation, Depression, Fatigue or weakness, Dry mouth, or Irregular menstrual periods
Upper tail probability P 0.25 0.2 0.15 0.1 0.05 0.03 0.02 0.01 z* 0.67 0.841 1.036 1.282 1.645 1.960 2.054 2.326 50% 60% 70% 80% 90% 95% 96% 98% Confidence level C Let’s calculate a 90% confidence interval for the population proportion of arthritis patients who suffer some “adverse symptoms.” What is the sample proportion ? ) ) 1

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IPS6e.PPT.Ch08 - Inference for Proportions Inference for a...

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