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Lecture Chapter5

# Lecture Chapter5 - Chapter 5 Introduction to Inference...

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Unformatted text preview: Chapter 5: Introduction to Inference: Estimation and Prediction Estimating Population Quantities: An Example Estimating the Effectiveness of a Medication A pharmaceutical company is testing the effectiveness of a new cholesterol-lowering medication. Specifically, they want to know (1) If the medication reduces low density lipoprotein (LDL) level in people with high LDL, and (2) On average, how much it reduces LDL among those people. Estimating Population Quantities: An Example To do so, the company’s scientists propose the following study. They will o Recruit 10 subjects with high levels of LDL cholesterol. o Make sure the subjects don’t take any cholesterol medication for two weeks to ensure an accurate baseline measurement. o Take an initial baseline reading. o Take a follow-up LDL measurement after the subject has been 30 days on the test medication. Estimating Population Quantities: An Example Here are the resulting data: Subject Baseline Follow-up LDL Decrease 1 160.5 168.1- 7 . 6 2 195.3 181.4 13.9 3 181.7 154.6 27.1 4 175.1 160.3 14.8 5 198.3 192.0 6.3 6 215.5 173.5 42.0 7 227.9 186.2 41.7 8 201.7 183.2 18.5 9 161.5 130.3 31.2 10 189.0 165.0 24.0 Estimating Population Quantities: An Example Suppose for the sake of argument, that there are only 10 people with high LDL in the world, and the company has tested them all. Can the company now answer its two questions: (1) Does the medication reduce LDL in people with high LDL? Subject Baseline Follow-up LDL Decrease 1 160.5 168.1- 7 . 6 2 195.3 181.4 13.9 3 181.7 154.6 27.1 4 175.1 160.3 14.8 5 198.3 192.0 6.3 6 215.5 173.5 42.0 7 227.9 186.2 41.7 8 201.7 183.2 18.5 9 161.5 130.3 31.2 10 189.0 165.0 24.0 It did in 9 of the 10. Or, putting it more scientifically, p , the proportion of the population for whom the drug lowers LDL, is 0.9. Estimating Population Quantities: An Example (2) On average, how much it does the medication change LDL among those people? Subject Baseline Follow-up LDL Decrease 1 160.5 168.1- 7 . 6 2 195.3 181.4 13.9 3 181.7 154.6 27.1 4 175.1 160.3 14.8 5 198.3 192.0 6.3 6 215.5 173.5 42.0 7 227.9 186.2 41.7 8 201.7 183.2 18.5 9 161.5 130.3 31.2 10 189.0 165.0 24.0 Answer: It reduced their LDL levels an average of 21.19 mg/dL. Or, putting it more scientifically, μ , the population mean decrease in LDL, equals 21.19. Estimating Population Quantities: An Example Because there were only 10 people with high LDL, the company was able to measure the change in LDL levels in all of them, and so could get exact answers to its questions. In this case the 10 people constitute the target population (which we will usually shorten to just population ): the group to which we want the conclusions to apply. Estimating Population Quantities: An Example Of course, there are many more than 10 people with high LDL levels; there are, in fact, millions, and these make up the target population for the company’s study. The company still wants to answer its two questions, but it cannot measure the LDL levels of everyone with high LDL....
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Lecture Chapter5 - Chapter 5 Introduction to Inference...

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