Week2B&3BMTB - ADM2304 One Proportion Dr Suren Phansalker Basic Theory(This is Strictly Optional When(n p > 5 and so is(n q > 5 pq p(1 p p

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ADM2304: One Proportion Dr. Suren Phansalker Basic Theory: (This is Strictly Optional!) When (n p > 5) and so is (n q > 5), (1 ) ~( ) , ( ) p pq p p pNE p p p nn μσ ⎛⎞ == = = ⎜⎟ ⎝⎠ /2 1 () pp Pz z p αα α σ −< < = ) { } ) ) 1 z p −− > >− =− 1 z p >> = () 1 P p zp p p σα +> > = , or P p p p < + = This is the CI: p p p σσ < + This theoretical CI is some times written as: Theoretical CI: ) p p pz p pz n ±= ± Obviously, ‘p’ is to be estimated and is not known. This problem is circumvented by using the sample-proportion p or . The CI is thus found by using the following expression. ˆ p Actual CI: ˆˆ ) ˆ p p pz sp pz n ± 1
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An Example: A random sample (Sample1 in C3) of 100 North American Males was taken. Their height was measured in inches. The following data was the result. Data Display Sample1 (in c3) 60.5 73.0 67.3 67.3 71.0 65.0 79.2 65.0 72.3 67.6 62.2 75.4 74.9 69.3 61.3 71.4 67.0 67.8 70.1 68.2 67.1 75.7 72.8 71.1 67.8 70.3 74.4 66.7 73.6 66.8 64.2 61.8 71.7 65.1 69.1 69.1 72.0 72.2 69.5 64.7 68.1 64.5 69.8 70.0 76.1 66.8 65.7 69.6 70.1 66.2 75.3 63.3 67.2 75.2 76.6 68.9 72.3 77.1 66.4 69.8 70.7 70.1 74.8 72.7 73.9 62.5 60.3 65.6 66.2 73.7 61.8 61.4 69.0 74.4 67.8 63.2 67.3 67.5 63.0 75.6 72.2 63.0 52.1 63.7 68.8 66.4 71.5 68.0 64.2 76.7 71.6 68.1 74.4 65.3 69.4 70.5 72.4 73.9 64.8 69.4 Any male with a height of 70” or more was considered “Tall”. Find: a. The 95% and 99% CIs for the population proportion of “Tall” people. b. Test the hypothesis that the population proportion is not 0.45. c. Test the hypothesis that the population proportion is more than 0.30. d. Test the hypothesis that the population proportion is less than 0.51. For ‘b’, ‘c’, and ‘d’ use a Level of Significance (LS) of 5% and 1%. This problem cannot be done without coding the data. Coding allows us to make groups; in this situation two groups: “Short” males less than 70” tall and “Tall” males 70” or more in height. It can be done readily as follows.
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This note was uploaded on 01/10/2012 for the course TEFLER 2304 taught by Professor Phansalker during the Winter '11 term at University of Ottawa.

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Week2B&amp;3BMTB - ADM2304 One Proportion Dr Suren Phansalker Basic Theory(This is Strictly Optional When(n p > 5 and so is(n q > 5 pq p(1 p p

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