Unit 10: Confidence Intervals

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 Main Concepts

• Confidence intervals are one way to make inference about a population using information from a sample.

• The confidence in a confidence interval is pre-determined by us. Confidence is in the method, not in the result.

• Most confidence intervals take this form: estimate plus or minus a chosen number of standard errors. The chosen number is selected to create the desired confidence level.

• Confidence intervals are computed from random samples and therefore they are random. The parameter is not random.

• The parameter is fixed (but unknown), and the estimate of the parameter is random (but observable). If the estimate is likely to be within two standard errors of the parameter, then the parameter is likely to be within two standard errors of the estimate. This is the foundation on which confidence intervals are based.

• The margin of error is affected by three factors: confidence level, sample size, and population standard deviation. You should understand how increasing or decreasing any of these factors will affect the margin of error. Sample sizes can be determined to achieve a particular margin or error.

• The margin of error that you read about in newspaper surveys (plus or minus 3 percentage points) is the same as the margin of error in a 95% confidence interval.

• Confidence intervals can be used to check the reasonableness of claims about the parameter. If someone claims the parameter is equal to 62, and 62 is not within your confidence interval, then this claim is suspect. This type of thinking will be made more formal and precise in the next unit.