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Chapter18_Part1

Chapter18_Part1 - Chapter 18 Part 1 Sampling Distribution...

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Chapter 18 – Part 1 Sampling Distribution Models for p ˆ

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Objectives Describe the sampling distribution of a proportion Understand that the variability of a statistic depends on the size of the sample Statistics based on larger samples are less variable Apply your knowledge of the Normal Distribution (Chapter 6) --- It's BACK!!!!!!
Review Chapter 6 – The Normal Distribution The Standard Normal Distribution - N(0,1) P(Z < 1.5) = 0.9332 P(Z > 2.4) = 1 – P(Z < 2.4) = 1-0.9918 = 0.0082 P(Z = 1.0) = 0 P(1.5 < Z < 2.4) = 0.9918 – 0.9332 = 0.0586

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Review Y~ N(70,3) 6293 . 0 ) 33 . ( ) 3 70 71 ( ) 71 ( = < = - < = < Z P Z P Y P 7486 . ) 67 . ( 1 ) 3 70 68 ( ) 68 ( = - < - = - = Z P Z P Y P 3779 . 2514 . 6293 . ) 68 ( ) 71 ( ) 71 68 ( = - = < - < = < < Y P Y P Y P
Review Chapter 12 – Sample Surveys Parameter (Population Characteristics) μ (mean) p (proportion) Statistic (Sample Characteristics) (sample mean) (sample proportion) p ˆ y

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Review Chapter 12 “Statistics will be different for each sample. These differences obey certain laws of probability (but only for random samples).” Chapter 14 Taking a sample from a population is a random phenomena. That means: The outcome is unknown before the event occurs The long term behavior is predictable
Example 2002 Senators Population Characteristics p = proportion of Democratic Senators μ = mean number of years in Senate Take SRS of size n = 10 Calculate Sample Characteristics = sample proportion of Democratic Senators = sample mean number of years in Senate y p ˆ

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Example 16.3 0.4 5 11.0 0.6 4 13.5 0.7 3 15.0 0.5 2 15.1 0.5 1 Sample p ˆ y
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Chapter18_Part1 - Chapter 18 Part 1 Sampling Distribution...

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