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A statistical range calculated around a sample statistic designed to contain the true population parameter a specified percentage of the time, most commonly $$95\%$$. Some researchers advocate using confidence intervals as an alternative to traditional null hypothesis testing because they are often more intuitive to interpret. Furthermore, a confidence interval inherently provides the data needed to perform a null hypothesis test; if a hypothetical population mean falls completely outside the calculated interval, the sample mean is considered statistically significantly different from that hypothetical value.

Confidence Interval

In survey research, a sample of about $$1,000$$ individuals is typically considered adequate to make accurate estimates, regardless of whether the broader population consists of a hundred thousand or a hundred million people. This is because a $$95\%$$ confidence interval depends only on the size of the sample itself, not on the size of the population. Furthermore, while increasing the sample size continues to shrink the confidence interval—meaning the sample statistic is likely closer to the true population value—it does so at a progressively slower rate. Consequently, the minor gains in statistical confidence achieved by surveying significantly more than $$1,000$$ people are generally not considered worth the additional time and financial cost.

Sample Size and Population Size

To illustrate a confidence interval, suppose a sample of $$20$$ university students provides a mean calorie estimate for a cookie of $$200$$, with a $$95\%$$ confidence interval ranging from $$160$$ to $$240$$. This indicates that there is a high probability ($$95\%$$) that the true mean calorie estimate for the entire population of university students falls somewhere between $$160$$ and $$240$$. Furthermore, this interval allows for hypothesis testing; any hypothetical population mean outside of this $$160$$ to $$240$$ range (such as a hypothetical value of $$250$$) would be considered statistically significantly different from the sample mean at the $$.05$$ alpha level.

Example of a Confidence Interval

By definition, a confidence interval is a statistical range calculated around a sample statistic that is designed to contain which of the following a specified percentage of the time?

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