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Sample Proportion and the Normal Approximation

This chapter discusses the use of sample proportions and the normal approximation in statistical analysis. It covers rules of thumb for when the population is large enough, applying the normal approximation to college admissions, and determining survey undercoverage.

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Sample Proportion and the Normal Approximation

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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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