### 9.4 Describing by Sampling

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• Math Help

In some texts, you might see statistical inference referred to as inferential statistics. Either term refers to the use of a sample to draw conclusions about a population. Note that infer means "to conclude by reasoning from something known or assumed." In the context of statistics, you infer information about the population from what you know about the sample.

When determining the confidence level, you might think that it is always best to choose 99%. However, 99% may not always be the best choice. Why? Because as the confidence level increases, the confidence interval widens. As the confidence interval widens, the precision of the estimate decreases. So, a 99% confidence level may produce an interval that is too wide and as a result conveys less information. For instance, it is better to be 95% confident that the average life of an automobile part is 6 to 8 years than to be 99% confident that the average life is 4 to 10 years (see figure below). As you construct confidence intervals, note that the goal is to obtain a narrow interval with a high level of confidence.

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• Checkpoint Solution

Using the Confidence Interval Calculator located in Tools, you can obtain the following.

• 90% Confidence Level: The population mean is 98.25°F ± 0.11°F, or between 98.14°F and 98.36°F.
• 95% Confidence Level: The population mean is 98.25°F ± 0.13°F, or between 98.12°F and 98.38°F.
• 99% Confidence Level: The population mean is 98.25°F ± 0.16°F, or between 98.09°F and 98.41°F.

The accepted human body temperature of 98.6°F does not lie within any of those confidence intervals. You cannot say with 100% confidence that the study does not allow for the accepted human body temperature of 98.6°F. However, you can say with 99% confidence that the population mean body temperature lies between 98.09°F and 98.41°F.

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