A Few Words About Error
Whatever we conclude, there is some chance that we've come to the wrong conclusion about the population proportion. This has nothing to do with computational mistakes or data entry errors (although it's always wise to double check) and everything to do with sampling variability. When we construct a 95% confidence interval, we're gambling that our one sample is from among the 95% whose sample proportions lie a modest distance from the actual parameter. By bad luck, we might draw a sample from among the other 5% of possible samples.
With hypothesis tests, the situation is slightly different because we can go astray whether we reject the null hypothesis or not. If our P -value is very small, there is still a chance that ...
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