# Chapter_19 - Chapter 19 Inference about a Population...

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BPS - 5th Ed. Chapter 19 1 Chapter 19 Inference about a Population Proportion

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BPS - 5th Ed. Chapter 19 2 The proportion of a population that has some outcome (“ success ”) is p . The proportion of successes in a sample is measured by the sample proportion : Proportions sample the in ns observatio of number total sample the in successes of number = p ˆ “p-hat”
BPS - 5th Ed. Chapter 19 3 Inference about a Proportion Simple Conditions

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BPS - 5th Ed. Chapter 19 4 Inference about a Proportion Sampling Distribution
BPS - 5th Ed. Chapter 19 5 Case Study Science News , Jan. 27, 1995, p. 451. Comparing Fingerprint Patterns

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BPS - 5th Ed. Chapter 19 6 Case Study: Fingerprints Fingerprints are a “sexually dimorphic trait… which means they are among traits that may be influenced by prenatal hormones.” It is known… Most people have more ridges in the fingerprints of the right hand. (People with more ridges in the left hand have “leftward asymmetry.”) Women are more likely than men to have leftward asymmetry. Compare fingerprint patterns of heterosexual and homosexual men.
BPS - 5th Ed. Chapter 19 7 Case Study: Fingerprints Study Results 66 homosexual men were studied. 20 (30%) of the homosexual men showed leftward asymmetry. 186 heterosexual men were also studied. 26 (14%) of the heterosexual men showed leftward asymmetry.

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BPS - 5th Ed. Chapter 19 8 Case Study: Fingerprints A Question Assume that the proportion of all men who have leftward asymmetry is 15%. Is it unusual to observe a sample of 66 men with a sample proportion ( ) of 30% if the true population proportion ( p ) is 15%? p ˆ
BPS - 5th Ed. Chapter 19 9 Case Study: Fingerprints Sampling Distribution s.d.) ( 0.044 66 0.15) 0.15(1 1 66 mean); ( 0.15 = = - = - = = = n p) p( n p

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BPS - 5th Ed. Chapter 19 10 Case Study: Fingerprints Answer to Question Where should about 95% of the sample proportions lie?
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