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# The Relationship between Confidence Levels and Confidence Intervals

As illustrated in the chart below, as the confidence level increases, so does the confidence interval. An analyst can be more certain of his or her result the wider the range within which it can fall. For example, one is likely to be 99% certain that one has properly estimated a person’s age if one guesses that the person is somewhere between 1 and 100 years old. However, one would be less certain if he or she guesses that the person’s age is between 40 and 60 years.

## 95%

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The above chart presents data collected from 22 facilities. The observed mean facility score was 9.2. The decision maker can be:

• î‚¾

95% certain that the true mean facility score is between 8.88 and 9.48

• î‚¾

90% certain it falls between 8.94 and 9.44

• î‚¾

85% certain it falls between 8.98 and 9.41

The Relationship between Confidence Interval Breadth and Confidence Level at Different Numbers of Inspections:

The confidence intervals are shown below for two states with an observed SQG achievement rate of 67% on an indicator. RI inspected 15 facilities, while Maine inspected 55 facilities. As can be seen, the confidence interval in RI was much wider than that of Maine.

90%

85%

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## The States Common Measures Project Final Report

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