10_07_11_2 - STAT 409 Examples for 10/07/2011 (2) Fall 2011...

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STAT 409 Examples for 10/07/2011 (2) Fall 2011 Testing Hypotheses about a Population Proportion p Null Alternative H 0 : p = p 0 vs. H 1 : p < p 0 Left – tailed. H 0 : p = p 0 vs. H 1 : p > p 0 Right – tailed. H 0 : p = p 0 vs. H 1 : p p 0 Two – tailed. 1. Let X have a Binomial distribution with the number of trials n = 8 and with probability of “success” p . We wish to test H 0 : p = 0.60 vs. H 1 : p < 0.60. Binomial distribution ( n = 8 ) CDF, P ( X x ): p n x 0.20 0.30 0.40 0.50 0.60 0.70 8 0 0.1678 0.0576 0.0168 0.0039 0.0007 0.0001 1 0.5033 0.2553 0.1064 0.0352 0.0085 0.0013 2 0.7969 0.5518 0.3154 0.1445 0.0498 0.0113 3 0.9437 0.8059 0.5941 0.3633 0.1737 0.0580 4 0.9896 0.9420 0.8263 0.6367 0.4059 0.1941 5 0.9988 0.9887 0.9502 0.8555 0.6846 0.4482 6 0.9999 0.9987 0.9915 0.9648 0.8936 0.7447 7 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 a) Suppose we observe X = 3. Find the p-value of this test.

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This note was uploaded on 10/13/2011 for the course STAT 409 taught by Professor Stephanov during the Fall '11 term at University of Illinois at Urbana–Champaign.

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10_07_11_2 - STAT 409 Examples for 10/07/2011 (2) Fall 2011...

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