... error.

A confidence interval is said to cover its parameter if the parameter lies within the interval. If

p^1.96  se(p^)pp^+1.96  se(p^)

then the interval covers p. The value 95%, or 0.95, is the coverage, or confidence level, of the interval. To alter the coverage, change the number of multiples of the standard error by using a different percentile of the normal distribution. For instance, the interval with z0.005 = 2.576 has 99% coverage because

P(p^2.576 se(p^)pp^+2.576 se(p^))=0.99

Notice that increasing ...

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