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Week2B&3BMTB2304 - ADM2304 One Proportion Dr Suren...

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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 p N E p p p n n μ σ = = = = / 2 / 2 1 ( ) p p P z z p α α α σ < < = / 2 / 2 ( 1){ } ( 1) ( 1) 1 ( ) p p P z z p α α α σ > > − = / 2 / 2 1 ( ) p p P z z p α α α σ > > − = ( ) / 2 / 2 ( ) ( ) 1 P p z p p p z p α α σ σ α + > > = , or ( ) / 2 / 2 ( ) ( ) 1 P p z p p p z p α α σ σ α < < + = This is the CI: / 2 / 2 ( ) ( ) p z p p p z p α α σ σ < < + This theoretical CI is some times written as: Theoretical CI: / 2 / 2 (1 ) ( ) p p p z p p z n α α σ ± = ± 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: / 2 / 2 ˆ ˆ (1 ) ˆ ˆ ˆ ( ) p p p z s p p z n α α ± = ± 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.
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