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L18-09 - The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL...

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11/12/09 Lecture 18 1 STOR 155 Introductory Statistics Lecture 18: Inference for a single proportion Section 8.1 The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL
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11/12/09 Lecture 18 2 Normal Approximation for Counts and Proportions Let X ~ B ( n, p ) and If n is large , then Rule of Thumb: np 10, n (1 - p ) 10. . / ˆ n X p ). / ) 1 ( , ( approx. is ˆ n -p p p N p
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11/12/09 Lecture 18 3 Confidence Interval for p Expression: where the margin of error Assumption: n is large Confidence level C determines m = z ã p ê(1 à p ê) =n p [ p ê à m ; p ê + m ] z ã
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11/12/09 Lecture 18 4 Hypothesis Testing for p For a hypothesized value , we want to test versus some alternative (1-sided or 2- sided). Recall the 4 steps … Step 1 : only need to specify Step 2 : Test statistic where p 0 H 0 : p = p 0 H a z = ( p ê à p 0 ) 0 û 0 = p 0 (1 à p 0 ) =n q
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11/12/09 Lecture 18 5 Hypothesis Testing for p (continued) Step 3 : The P -value will be equal to P ( Z > z ) for 1-sided (upper tail) P ( Z < z ) for 1-sided (lower tail) 2 P ( Z > | z| ) for 2-sided Step 4 : Compare the P -value with the significance level and draw your conclusion. H a : p > p 0 H a : p < p 0 H a : p 6 = p 0 ë
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11/12/09 Lecture 18 6 “Biased” one -Euro Coin? A group of statistics students spun the Belgian one-Euro coin 250 times, and heads came up 140
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