Confidence Intervals: The Basics
     LEARNING TARGETS
     By the end of this section, you should be able to:
     IDENTIFY an appropriate point estimator and CALCULATE the value of a point 
      estimate.
     INTERPRET a confidence interval in context.
     DETERMINE the point estimate and margin of error from a confidence interval.
     USE a confidence interval to MAKE a decision about the value of a parameter.
     INTERPRET a confidence level in context.
     DESCRIBE how the sample size and confidence level affect the margin of error.
     EXPLAIN how practical issues like nonresponse, undercoverage, and response 
      bias can affect the interpretation of a confidence interval.
                                   Starnes/Tabor, The Practice of Statistics
     Point Estimators
     A point estimator is a statistic that provides an estimate of a population
     A point estimator is a statistic that provides an estimate of a population
     parameter. 
     parameter. 
     The value of that statistic from a sample is called a point estimate.
     The value of that statistic from a sample is called a point estimate.
                                   Starnes/Tabor, The Practice of Statistics
        Point Estimators
        Problem: Identify the point estimator you would use to estimate
         Problem: Identify the point estimator you would use to estimate
        the parameter in each of the following settings and calculate the                       s
         the parameter in each of the following settings and calculate the                      e
                                                                                                g
                                                                                                a
        value of the point estimate.                                                            m
         value of the point estimate.                                                           I
                                                                                                 
                                                                                                y
                                                                                                t
                                                                                                t
        (a) Quality control inspectors want to estimate the mean lifetime                       e
         (a) Quality control inspectors want to estimate the mean lifetime                      G
                                                                                                /
                                                                                                a
            µ of the AA batteries produced each hour at a  factory. They                        v
             µ of the AA batteries produced each hour at a  factory. They                       o
                                                                                                p
                                                                                                o
                                                                                                P
            select a random sample of 50 batteries during each hour of production and           T
             select a random sample of 50 batteries during each hour of production and 
            then drain them under conditions that mimic normal use. Here are the 
             then drain them under conditions that mimic normal use. Here are the 
            lifetimes (in hours) of the batteries from one such sample:
             lifetimes (in hours) of the batteries from one such sample:
                           16.73 15.60 16.31 17.57 16.14 17.28 16.67 17.28 17.27 17.50
                           16.73 15.60 16.31 17.57 16.14 17.28 16.67 17.28 17.27 17.50
                           15.59 17.54 16.46 15.63 16.82 17.16 16.62 16.71 16.69 17.98
                           15.59 17.54 16.46 15.63 16.82 17.16 16.62 16.71 16.69 17.98
                           15.99 15.64 17.20 17.24 16.68 16.55 17.48 15.58 17.61 15.98
                           15.99 15.64 17.20 17.24 16.68 16.55 17.48 15.58 17.61 15.98
                           15.46 16.50 16.19 16.36 17.80 16.61 16.99 16.93 16.01 16.46
                           15.46 16.50 16.19 16.36 17.80 16.61 16.99 16.93 16.01 16.46
                           17.54 17.41 16.91 16.60 16.78 15.75 17.31 16.50 16.72 17.55
                           17.54 17.41 16.91 16.60 16.78 15.75 17.31 16.50 16.72 17.55
                                                                    Starnes/Tabor, The Practice of Statistics
        Point Estimators
        Problem: Identify the point estimator you would use to estimate
         Problem: Identify the point estimator you would use to estimate
        the parameter in each of the following settings and calculate the                       s
         the parameter in each of the following settings and calculate the                      e
                                                                                                g
                                                                                                a
        value of the point estimate.                                                            m
         value of the point estimate.                                                           I
                                                                                                 
                                                                                                y
                                                                                                t
                                                                                                t
        (a) Quality control inspectors want to estimate the mean lifetime                       e
         (a) Quality control inspectors want to estimate the mean lifetime                      G
                                                                                                /
                                                                                                a
            µ of the AA batteries produced each hour at a  factory. They                        v
             µ of the AA batteries produced each hour at a  factory. They                       o
                                                                                                p
                                                                                                o
                                                                                                P
            select a random sample of 50 batteries during each hour of production and           T
             select a random sample of 50 batteries during each hour of production and 
            then drain them under conditions that mimic normal use. Here are the 
             then drain them under conditions that mimic normal use. Here are the 
            lifetimes (in hours) of the batteries from one such sample:
             lifetimes (in hours) of the batteries from one such sample:
                           16.73 15.60 16.31 17.57 16.14 17.28 16.67 17.28 17.27 17.50
                           16.73 15.60 16.31 17.57 16.14 17.28 16.67 17.28 17.27 17.50
                           15.59 17.54 16.46 15.63 16.82 17.16 16.62 16.71 16.69 17.98
                           15.59 17.54 16.46 15.63 16.82 17.16 16.62 16.71 16.69 17.98
                           15.99 15.64 17.20 17.24 16.68 16.55 17.48 15.58 17.61 15.98
                           15.99 15.64 17.20 17.24 16.68 16.55 17.48 15.58 17.61 15.98
                           15.46 16.50 16.19 16.36 17.80 16.61 16.99 16.93 16.01 16.46
                           15.46 16.50 16.19 16.36 17.80 16.61 16.99 16.93 16.01 16.46
                           17.54 17.41 16.91 16.60 16.78 15.75 17.31 16.50 16.72 17.55
                           17.54 17.41 16.91 16.60 16.78 15.75 17.31 16.50 16.72 17.55
              (a) Use the sample mean  as a point estimator for the population 
              (a) Use the sample mean  as a point estimator for the population 
               
               
                 mean µ. The point estimate is
                  mean µ. The point estimate is
                                                                    Starnes/Tabor, The Practice of Statistics
        Point Estimators
        Problem: Identify the point estimator you would use to estimate
        Problem: Identify the point estimator you would use to estimate
        the parameter in each of the following settings and calculate the                    s
        the parameter in each of the following settings and calculate the                    e
                                                                                             g
                                                                                             a
        value of the point estimate.                                                         m
        value of the point estimate.                                                         I
                                                                                              
                                                                                             y
                                                                                             t
                                                                                             t
        (b) What proportion p of U.S. adults would classify themselves as                    e
        (b) What proportion p of U.S. adults would classify themselves as                    G
                                                                                             /
                                                                                             a
            vegan or vegetarian? A Pew Research Center report surveyed                       v
            vegan or vegetarian? A Pew Research Center report surveyed                       o
                                                                                             p
                                                                                             o
                                                                                             P
            1473 randomly selected U.S. adults. Of these, 124 said they were vegan or        T
            1473 randomly selected U.S. adults. Of these, 124 said they were vegan or 
            vegetarian.
            vegetarian.
                                                                  Starnes/Tabor, The Practice of Statistics