Exercise 5.2

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1. Consider a learned hypothesis, h, for some boolean concept. When h is tested on a set of 100 examples, it classifies 83 correctly. What is the standard deviation and the 95% confidence interval for the true error rate for Error _D ( h )?
   
   

   17 / 100	=	0.17
   100 ( 0.17 )( 1 - 0.17 )	=	14.11
   square root ( 14.11 )	=	3.76
   3.76 / 100	=	0.0376
   	=	standard deviation estimate for Error D ( h )
   95% confidence interval for Error D ( h ) =
   	Error D ( h ) +- 1.96 * ( square root [ Error D ( h ) * ( 1 - Error D ( h ) ) / n ] )
   	=	0.17 +- 1.96 ( square root [ 0.17 * ( 1 - 0.17 ) / 100 ] )
   	=	0.17 +- 0.0736

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