Statistics for Business: Decision Making and Analysis, 3rd Edition

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z-interval

A confidence interval based on using a normal model for the sampling distribution.

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

$$\widehat{p}-1.96 \text{se}\left(\widehat{p}\right)\le p\le \widehat{p}+1.96 \text{se}\left(\widehat{p}\right)$$

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 z_0.005 = 2.576 has 99% coverage because

coverage or confidence level

Probability of a random sample in which the confidence interval holds the parameter. Most often, the coverage is 0.95.

$$P\left(\widehat{p}-2.576 \text{se}\left(\widehat{p}\right)\le p\le \widehat{p}+2.576 \text{se}\left(\widehat{p}\right)\right)=0.99$$

Notice that increasing ...