Confidence Intervals for a Population 
       Confidence Intervals for a Population 
       Proportion
       Proportion
       Section 7.3
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                                                                           Objectives
            1. Construct a confidence interval for a population proportion
            2. Find the sample size necessary to obtain a confidence 
                     interval of a given width
            3. Describe a method for constructing confidence intervals with 
                     small samples
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       Objective 1*
       Objective 1*
       Construct a confidence interval for a population 
       proportion
       *(Tables)
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                          Confidence Interval for a Proportion*
                                                                           The music organization Little Kids Rock 
                                                                           surveyed 517 music teachers, and 403 of 
                                                                           them said that video games like Guitar 
                                                                           Hero and Rock Band, in which players try 
                                                                           to play music in time with a video image, 
                                                                           have a positive effect on music education. 
                                                                           Assuming these teachers to be a random 
                                                                           sample of U.S. music teachers, we would 
                                                                           like to construct a confidence interval for 
                                                                           the proportion of music teachers who 
                                                                           believe that music video games have a 
                                                                           positive effect on music classrooms.
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                                                                            Notation*
      •       
      We use the following notation:
      •  is the population proportion of individuals who are in a 
           specified category.
      •  is the number of individuals in the sample who are in the 
           specified category.
      •  is the sample size.
      •  is the sample proportion of individuals who are in the 
           specified category.  is defined as 
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