### 9.4 Describing by Sampling

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• Math Help

As you read the "Inferring from a Sample" box on page 434, note that the margin of error in the estimated population mean refers only to the amount of error that occurs because of chance.

As you read Example 1, note the following.

• The mean and standard deviation are given in the histogram. Recall from Section 9.3 that "SD" is an abbreviation for "standard deviation."
• The Confidence Interval Calculator is located in Tools.
• In the solution, the symbol "±" is read as "plus or minus." So, the phrase "80 cm ± 3.1 cm" is read as "80 centimeters plus or minus 3.1 centimeters."

A confidence interval is a range of values used to estimate the value of an unknown population mean. (Note that a confidence interval can also be constructed for other parameters, such as standard deviation.) A confidence level is the probability that the interval contains the population mean. Suppose a large number of different samples of the same size are collected and a 90% confidence interval is created for each sample. It should be expected that 90% of the intervals will contain the population mean. This is illustrated in the figure below.

For instance, consider the 90% confidence interval found in Example 1, 80 cm ± 3.1 cm. This means you can be 90% confident that the population mean shoulder height of male black bears lies between 76.9 centimeters and 83.1 centimeters.

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• Checkpoint Solution

Use the Confidence Interval Calculator located in Tools.

• 99% Confidence Level: The population mean is 80 cm ± 4.9 cm.

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