Exercise 5.3

Suppose hypothesis h commits r = 10 errors over a sample of n = 65 independently drawn examples.

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1. What is the 90% confidence interval (two-sided) for the true error rate?
   
   

   10 / 65	=	0.15
   90% interval	=	0.15 +- 1.64 ( square root [ 0.15 * ( 1 - 0.15 ) / 65 ] )
   	=	0.15 +- 0.073

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2. What is the 95% one-sided interval (i.e., what is the upper bound U such that error_D(h) <= U with 95% confidence)?
   
   

   upper bound	=	0.15 + 0.073
   	=	0.223

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3. What is the 90% one-sided interval?
   
   

   80% interval	=	0.15 +- 1.28 ( square root [ 0.15 * ( 1 - 0.15 ) / 65 ] )
   	=	0.15 +- 0.056
   90% upper bound	=	0.15 + 0.056
   	=	0.206

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