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Chapter 9.2: Sample Proportion

Chapter 9.2: Sample Proportion. Mr. Lynch AP Statistics. Sample Proportions. In what year did Christopher Columbus “discover” America? What is our classes p-hat? 210 of the 501 sampled in a Gallup Poll knew this. Rules of Thumb . RULE OF THUMB 1:

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Chapter 9.2: Sample Proportion

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  1. Chapter 9.2: Sample Proportion Mr. Lynch AP Statistics

  2. Sample Proportions • In what year did Christopher Columbus “discover” America? • What is our classes p-hat? • 210 of the 501 sampled in a Gallup Poll knew this.

  3. Rules of Thumb • RULE OF THUMB 1: • You can only use the standard deviation formula of the population is large enough. Specifically N 10n • RULE OF THUMB 2: • You can only use A NORMAL APPROXIMATION to the propoprtion sampling distribution with values of n and p if np10 AND nq10

  4. The Normal Approximation • When n is LARGE, the Sampling Distribution of is approximately normal • EXAMPLE 9.7: APPLYING TO COLLEGE • SRS OF n = 1500; p = .35 • Check Rules of Thumb • P(the random sample will produce a percentage within 2% of the actual population proportion of 35%)

  5. The Normal Approximation • Draw it! • Standardize the p-hat values • Re-draw with the new z-scores • Calculate Area with table or normalcdf

  6. SURVEY UNDERCOVERAGE • EXAMPLE 9.8 SURVEY UNDERCOVERAGE? • 11% US adults are black • A recent national sample of 1500 adults had only a 9.2% black representation • Should we suspect racial discrimination or some sort of under-coverage?

  7. SURVEY UNDERCOVERAGE • Rules of Thumb • Draw it! • Standardize the p-hat value • Re-draw with the new z-score • Calculate Area with table or normalcdf

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