Alan wants to estimate the proportion of adults who walk to work. In a survey of 10 adults, he finds 0 who walk to work. Explain why a 95% confidence interval using the normal model yields silly results. Then compute and interpret a 95% confidence interval for the proportion of adults who walk to work using Agresti and Coull’s method.

To deal with issues such as the distribution of  not following a normal distribution, A. Agresti and B. Coull proposed a modified approach to constructing confidence intervals for a proportion. A (1 - α).100% confidence interval for p is given by

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Lower bound: P - Zn+4 P(I - T) Upper bound: p+Z2 p(1-p) V n+ 4 x 2 n+ 4 where