Confidence Intervals With Proportions and Percentages

The principles that guide the construction of confidence intervals around means also apply to confidence intervals around proportions and percentages. There is no difference in the procedure used for proportions versus that for percentages—percentages simply have to be converted to proportions before they are plugged into the CI formula. For this reason, we will speak in terms of proportions for the remainder of the discussion.

There are sampling distributions for proportions just as there are for means. Because of sampling error, a

sample proportion (symbolized , pronounced “p hat”) cannot be assumed to equal the population proportion (symbolized as an uppercase P) , so confidence intervals must be created in order to estimate the population values with a certain level of probability.

What Factors Influence Repeat Offenders’ Completion of a “Driving Under the Influence” Court Program?

Specialized courts are an increasingly popular way for dealing with low-level offenders, especially those who have drug or mental- health problems. The rationale is that these people should not be incarcerated in jail or prison and should instead be allowed to remain in the community and complete one or more treatment programs to help them with their problems. Judges are responsible for supervising the defendants in these courts. Defendants typically appear before the judge every month or two, and the judge praises them when they have done well in their program and reprimands them when they have failed to follow through on an assignment. Usually, charges are dropped when defendants complete the program successfully, and those who drop out or are removed for noncompliance get sentenced to a previously agreed-on penalty (such as a specified jail or probation term).